Publications of Andreas Cap

Book(s)

Articles

  1. Partial AHS-Structures, their Cartan description and partial BGG sequences (joint with M.A. Wasilewicz), preprint arXiv:2410.10410.
     
  2. Flat extensions of principal connections and the Chern-Simons 3-form (joint with K. Flood and T. Mettler), preprint arXiv:2409.12811.
     
  3. On Relative Tractor Bundles (joint with Z. Guo and M.A. Wasilewicz), SIGMA Symmetry Integrability Geom. Methods Appl. 20 (2024), paper no. 108, 19 pp., DOI: 10.3842/SIGMA.2024.108. Published version available online here. Also available as preprint arXiv:2405.13614.
     
  4. Poisson transforms, the BGG complex, and discrete series representations of SU(n+1,1) (joint with P. Julg and C. Harrach), preprint arXiv:2402.08262.
     
  5. Bounded Poincaré operators for twisted and BGG complexes (joint with K. Hu), J. Math. Pures Appl. 179 (2023) 253-266, DOI: 10.1016/j.matpur.2023.09.008 published version available online here.
     
  6. Induced almost para-Kähler Einstein metrics on cotangent bundles (joint with T. Mettler), to appear in Quarterly J. Math., DOI:10.1093/qmath/haae047 electronically available at arXiv:2301.03217.
     
  7. Bundles of Weyl structures and invariant calculus for parabolic geometries (joint with J. Slovak), in I.S. Krasil'shchik et. al. (eds.) "The Diverse World of PDEs: Geometry and Mathematical Physics", Contemp. Math. 788 (2023), 53-72, DOI: 10.1090/conm/788/15819 electronically available as preprint arXiv:2210.16652.
     
  8. BGG sequences with weak regularity and applications (joint with K. Hu), Found. Comput. Math. 24 (2024), 1145-1184, DOI: 10.1007/s10208-023-09608-9, published version available here.
     
  9. A Boundary-Local Mass Cocycle and the Mass of Asymptotically Hyperbolic Manifolds (joint with A.R Gover), Comm. Math. Phys. 405 (2024) article 233, DOI: 10.1007/s00220-024-05079-3, published version freely avilable online here.
     
  10. Geometric Theory of Weyl Structures (joint with T. Mettler), Commun. Contemp. Math. 25 No. 7 (2023) article 2250026, DOI: 10.1142/S0219199722500262, electronically available at arXiv:1908.10325.
     
  11. A Poisson transform adapted to the Rumin complex (joint with P. Julg and C. Harrach), J. Topol. Anal. 14 No. 3 (2022) 615-653, DOI: 10.1142/S1793525320500570, electronically available at arXiv:1904.00635.
     
  12. C1 Deformations of almost-Grassmannian structures with strongly essential symmetry (joint with K. Melnick), Transform. Groups 26 no. 4 (2021) 1169-1187, DOI: 10.1007/s00031-020-09584-2, published version available via SharedIt here, also available online at arXiv:1902.01801.
     
  13. Parabolic Compactification of Homogeneous Spaces (joint with A.R Gover and M. Hammerl), J. Inst. Math. Jussieu 20 no. 4 (2021) 1371-1408, DOI: 10.1017/S1474748019000513, published version availbable via Cambridge Core Share. Also availabel online via arXiv:1807.04556.
     
  14. On C-class equations (joint with B. Doubrov and D. The), Commun. Anal. Geom. 30 No. 10 (2022) 2231-2266, DOI: 10.4310/CAG.2022.v30.n10.a2, electronically available at arXiv:1709.01130.
     
  15. On canonical Cartan connections associated to filtered G-structures, electronically available at arXiv:1707.05627.
     
  16. Parabolic conformally symplectic structures III; Invariant differential operators and complexes (joint with T. Salac), Doc. Math. 24 (2019) 2203-2240, published version available online via elibm.
     
  17. Parabolic conformally symplectic structures II; parabolic contactification (joint with T. Salac), Ann. Mat. Pura Appl. 197 no. 4 (2018) 1175-1199, published version (via SharedIt) open access, also electronically available at arXiv:1605.01897.
     
  18. Parabolic conformally symplectic structures I; definition and distinguished connections (joint with T. Salac), Forum Math. 30, 3 (2018) 733-751, electronically available at arXiv:1605.01161.
     
  19. C-Projective Compactification; (quasi-)Kähler Metrics and CR boundaries (joint with A.R. Gover), Amer. J. Math. 141 3 (2019) 813-856, electronically available at arXiv:1603.07039.
     
  20. Relative BGG sequences; II. BGG machinery and invariant operators (joint with V. Soucek) Adv. Math. 320 (2017) 1009-1062, free access to published version until Dec. 6, 2017 here, permanently electronically available at arXiv:1510.03986.
     
  21. Relative BGG sequences; I. Algebra (joint with V. Soucek) J. Algebra 463 (2016) 188-210, electronically available at arXiv:1510.03331.
     
  22. Conformal Holonomy Equals Ambient Holonomy (joint with A.R. Gover, C.R. Graham, and M. Hammerl), Pacific J. Math. 285 no. 2 (2016), 303-318, electronically available at arXiv:1504.00914.
     
  23. Scalar Curvature and Projective Compactness (joint with A.R. Gover), J. Geom. Phys. 98 (2015) 475-481, available online at arXiv:1409.1698.
     
  24. Projective Compactness and Conformal Boundaries (joint with A.R. Gover) Math. Ann. 366 no. 3-4 (2016) 1587-1620, published version (via SharedIt), also available online at arXiv:1406.4225.
     
  25. Pushing down the Rumin complex to locally conformally symplectic quotients (joint with T. Salac), Differential Geom. Appl. 35 Supplement (2014) 255-265, available online at arXiv:1312.2712.
     
  26. Projective Compactifications and Einstein metrics (joint with A.R. Gover) J. Reine Angew. Math. 717 (2016) 47-75, electronically available at arXiv:1304.1869.
     
  27. Essential Killing fields of parabolic geometries: projective and conformal structures (joint with K. Melnick) Centr. Europ. J. Math 11, 12 (2013) 2053-2061, published version, also available as Preprint ESI 2393 [ PDF ]
     
  28. Essential Killing fields of parabolic geometries (joint with K. Melnick), Indiana Univ. J. Math. 62 no. 6 (2013) 1917-1953, published version also electronically available as Preprint ESI 2388 [ PDF ]
     
  29. Einstein metrics in projective geometry (joint with A.R. Gover and H. Macbeth) Geom. Dedicata 168 No. 1 (2014) 235-244, published version (via SharedIt), also electronically available as Preprint ESI 2373 [ PDF ]
     
  30. Normal BGG solutions and polynomials (joint with A.R. Gover and M. Hammerl) Internat. J. Math. 23 No. 11 (2012) 1250117, 29pp., electronically available as Preprint ESI 2348 [ PDF ]
     
  31. Holonomy reductions of Cartan geometries and curved orbit decompositions (joint with A.R. Gover and M. Hammerl) Duke Math. J. 163, no. 5 (2014) 1035-1070, electronically available as Preprint ESI 2308 [ PDF ]
     
  32. Projective BGG equations, algebraic sets, and compactifications of Einstein geometries (joint with A.R. Gover and M. Hammerl) J. London Math. Soc. 86 no. 2 (2012) 433-454, electronically available as [  published version ] or as Preprint ESI 2249 [ PDF ]
     
  33. Equivariant quantizations for AHS-structures (joint with J. Silhan), Adv. Math. 224 (2010) 1717-1734, published version (via open archive), also electronically available as Preprint ESI 2136 [ PDF ]
     
  34. Contact projective structures and chains (joint with V. Zadnik), Geom. Dedicata 146, 1 (2010) 67-83, published version (via ShearedIt), also electronically available as Preprint ESI 2058 [ PDF ]
     
  35. Conformally invariant operators via curved Casimirs: examples (joint with A. Rod Gover and V. Soucek), Pure Appl. Math. Q. 6, 3 (2010) 693-714, electronically available as Preprint ESI 2049 [ PDF ]
     
  36. On automorphism groups of some types of generic distributions (joint with K. Neusser), Differential Geom. Appl. 27 (2009) 769-779, published version (via open archive), also electronically available as Preprint ESI 2036 [ PDF ]
     
  37. AHS-structures and affine holonomies, Proc. Amer. Math. Soc. 137 no. 3 (2009) 1073-1080, published version, also available as Preprint ESI 2021 [ PDF ]
     
  38. On Nurowski's Conformal Structure Associated to a Generic Rank Two Distribution in Dimension Five (joint with K. Sagerschnig), J. Geom. Phys. 59 (2009) 901-912, electronically available as Preprint ESI 1963 [ PDF ]
     
  39. Curved Casimir operators and the BGG machinery (joint with V. Soucek), SIGMA 3 (2007) 111, 17 pages, available online via http://www.emis.de/journals/SIGMA/2007/111/
     
  40. The Heisenberg group, SL(3,R), and Rigidity (joint with M.G. Cowling, F. De Mari, M.G. Eastwood, and R. McCallum), in "Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory: In Honour of Roger E. Howe", edited by Jian-Shu Li, Eng-Chye Tan, Nolan Wallach and Chen-Bo Zhu, Singapore University Press and World Scientific Publishing (2007) 49-62. electronically available as ESI Preprint 1913: [ PDF ]
     
  41. A holonomy characterisation of Fefferman spaces (joint with A.R. Gover), Ann. Glob. Anal. Geom. 38 no. 4 (2010) 399-412, published version (via SharedIt), also electronically available as ESI Preprint 1875: [ PDF ]
     
  42. CR-Tractors and the Fefferman Space (joint with A.R. Gover), Indiana Univ. Math. J. 57 No. 5 (2008) 2519-2570, published version in PDF
     
  43. Overdetermined Systems, Conformal Geometry, and the BGG Complex, in M.G. Eastwood, W. Miller (eds.) "Symmetries and Overdetermined Systems of Partial Differential Equations", The IMA Volumes in Mathematics and its Applications 144, Springer (2008), 1-25. electronically available as ESI Preprint 1849: [ PDF ]
     
  44. On left invariant CR structures on SU(2), Arch. Math. (Brno) 42 (2006) Supplement 185-195 ("Proceedings of the Winter School on Geometry and Physics, Srni 2006"), electronically available via the electronic libarary of the EMS: [ PDF ]
     
  45. Infinitesimal Automorphisms and Deformations of Parabolic Geometries, JEMS 10, 2 (2008) 415-437, electronicallly available as ESI Preprint 1684: [ PDF ]
     
  46. Subcomplexes in Curved BGG-Sequences (joint with V. Soucek), Math. Ann. 354 No. 1 (2012) 111-136, published version (via SharedIt), also electronically availabe as ESI Preprint 1683: [ PDF ]
     
  47. On the Geometry of Chains (joint with V. Zadnik), J. Differential Geom. 82, 1 (2009) 1-33, electronically available as ESI Preprint 1651: [ PDF ]
     
  48. Prolongations of Geometric Overdetermined Systems (joint with T. Branson, M. Eastwood, and R. Gover), Internat. J. Math. 17 No. 6 (2006) 641-664, electronically available as ESI Preprint 1458: [ PDF ]
     
  49. Two constructions with parabolic geometries, in "Proceedings of the 25th Winter School on Geometry and Physics, Srni 2005" Rend. Circ. Mat. Palermo Suppl. ser. II, 79 (2006) 11-37, electronically available as ESI Preprint 1645: [ PDF ]
     
  50. Automorphism groups of parabolic geometries, in "Proceedings of the 24th Winter School on Geometry and Physics, Srni 2004" Rend. Circ. Mat. Palermo Suppl. ser. II 75 (2005) 233-239, electronically available as ESI Preprint 1478: [ PDF ]
     
  51. Correspondence spaces and twistor spaces for parabolic geometries, J. Reine Angew. Math. 582 (2005) 143-172, electronically available as ESI Preprint 989: [ PDF ]
     
  52. On Distinguished Curves in Parabolic Geometries (joint with J. Slovak and V. Zadnik), Transform. Groups 9 no. 2 (2004) 143-166, published version (via SharedIt), also electronically available as ESI Preprint 1346: [ PDF ]
     
  53. Standard tractors and the conformal ambient metric construction (joint with A.R. Gover), Ann. Global Anal. Geom. 24, 3 (2003) 231-259, published version (via SharedIt), also electronically available as ESI Preprint 1177: [ PDF ]
     
  54. Some special geometry in dimension six (joint with M. Eastwood), in "Proceedings of the Winter School on Geometry and Physics, Srni 2002" Rend. Circ. Mat. Palermo Suppl. ser. II 71 (2003) 93-98 electronically available as ESI Preprint 851: [ PDF ]
     
  55. Weyl structures for parabolic geometries (joint with J. Slovak), Math. Scand. 93, 1 (2003) 53-90, electronically available as ESI Preprint 801: [ PDF ]
     
  56. Parabolic geometries, CR-tractors, and the Fefferman construction, Differential Geom. Appl. 17 (2002) 123-138, published version (via open archive), also electronically available as ESI Preprint 1084: [ PDF ]
     
  57. Partially integrable almost CR manifolds of CR dimension and codimension two (joint with G. Schmalz), in "Lie Groups Geometric Structures and Differential Equations - One Hundred Years after Sophus Lie", Advanced Studies in Pure Mathematics 37, Mathematical Society of Japan, Tokyo, (2002), 45-79, electronically available as ESI Preprint 937: [ PDF ]
     
  58. Tractor calculi for parabolic geometries (joint with A.R. Gover), Trans. Amer. Math. Soc. 354 (2002), 1511-1548, published version available online free of charge [PDF]
     
  59. Bernstein-Gelfand-Gelfand Sequences (joint with J. Slovak and V. Soucek) Ann. of Math. 154, no. 1 (2001) 97-113, extended version available as ESI Preprint 722: [ PDF ]
     
  60. Almost CR-manifolds of CR-dimension and codimension two RIMS Kokyuroku 1150 (2000), 54-62, Postscript
     
  61. Tractor bundles for irreducible parabolic geometries (joint with A.R. Gover), SMF, Séminaires et Congrès, numéro 4, (2000), 129-154, electronically available as ESI Preprint 865: [ PDF ]
     
  62. Invariant Operators on Manifolds with Almost Hermitian Symmetric Structures, III. Standard Operators (joint with J. Slovak and V. Soucek) Diferential Geom. Appl. 12 No. 1 (2000) 51-84, published version (via open archive), also electronically available as ESI Preprint 613: [ PDF ]
     
  63. Parabolic Geometries and Canonical Cartan Connections (joint with H. Schichl), Hokkaido Math. J. 29 No.3 (2000) 453-505, electronically available as ESI Preprint 450: [ PDF ]
     
  64. Invariant Operators on Manifolds with Almost Hermitian Symmetric Structures, II. Normal Cartan Connections (joint with J. Slovak and V. Soucek), Acta Math. Univ. Comenian. 66 no. 2 (1997) 203-220, electronically available: [ DVI , PDF , Compressed Postscript ]
     
  65. Invariant Operators on Manifolds with Almost Hermitian Symmetric Structures, I. Invariant Differentiation (joint with J. Slovak and V. Soucek) Acta Math. Univ. Comenian. 66 no. 1 (1997) 33-69, electronically available: [ DVI , PDF , Compressed Postscript ]
     
  66. Translation of natural operators on manifolds with AHS-structures Arch. Math. (Brno) 32 no. 4 (1996) 249-266, electronically available: [ Postscript ]
     
  67. On local flatness of manifolds with AHS-structures (joint with J. Slovak) in "Proceedings of the 15th Winter School on Geometry and Physics, Srni 1995" Rend. Circ. Mat. Palermo Suppl. ser. II 43 (1996) 95-101, electronically available as ESI preprint 227: [ PDF ]
     
  68. Characteristic classes for A-bundles (joint with H. Schichl), in "The Proceedings of the Winter School on Geometry and Physics (Srni 1994)" Rend. Circ. Mat. Palermo Suppl. ser. II 39 (1996) 57-71
     
  69. A note on endomorphisms of modules over reductive Lie groups and algebras in "Proceedings of the Conference Differential Geometry and its Applications, Brno 1995", 127-131, electronically available: [ Abstract , DVI , Postscript ]
     
  70. On Twisted Tensor Products of Algebras (joint with H. Schichl and J. Vanzura) Commun. Algebra 23 no. 12 (1995) 4701-4735, electronically available as ESI Preprint 163: [ PDF ]
     
  71. On multilinear operators commuting with Lie derivatives (joint with J. Slovak) Ann. Global Anal. Geom. 13 (1995) 251-279, electronically available as ESI Preprint 56: [ PDF ]
     
  72. A quantum group like structure on non commutative 2-tori (joint with P.W. Michor and H. Schichl) Lett. Math. Phys. 28 (1993), 251-255.
  73. Towards the Chern-Weil homomorphism in non commutative differential geometry (joint with P.W. Michor) in "Proceedings of the 21st international Conference on Differential Geometric Methods in Theoretical Physics", Int. Jour. Mod. Physics A (Proc. Suppl.) 3A (1993), 210-213
     
  74. Report on K-Theory for Convenient Algebras II in "The Proceedings of the Winter School Geometry and Topology (Srni 1992)", Rend. Circ. Mat. Palermo Suppl. ser. II 32 (1993) 175-184
     
  75. The Frölicher-Nijenhuis Bracket in Non Commutative Differential Geometry (joint with A. Kriegl, P.W. Michor, and J. Vanzura), Acta Math. Univ. Comenian., LXII No. 1 (1993), 17-49 , electronically available: [ DVI , PDF , Compressed Postscript ]
     
  76. Report on K-Theory for Convenient Algebras in "Proceedings of the Winter School Geometry and Physics (Srni 1991)'', Rend. Circ. Mat. Palermo Suppl. ser. II 30 (1993) 55-63
     
  77. Infinitesimally Natural Operators are Natural (joint with J. Slovak), Differential Geom. Appl. 2 (1992) 45-55, published version (via open archive)
     
  78. Natural operators between vector valued differential forms, in "Proceedings of the Winter School on Geometry and Physics (Srni, 1990)" Rend. Circ. Mat. Palermo Suppl. ser. II 26 (1991) 113-121
     
  79. All linear and bilinear natural concomitants of vector valued differential forms, Comment. Math. Univ. Carolin. 31 No. 3 (1990), 567-587