Séminaire Lotharingien de Combinatoire, 80B.39 (2018), 12 pp.
Yann Palu, Vincent Pilaud and Pierre-Guy Plamondon
Non-Kissing Complexes for Gentle Algebras
Abstract.
We introduce the non-kissing complex of any gentle bound quiver.
This complex provides a powerful combinatorial model for support τ-tilting theory over gentle algebras, and it generalizes and unifies the previously considered situations of quivers defined from subsets of the grid or from dissections of a polygon (both generalizing the classical associahedron).
In this extended abstract, we report on lattice theoretic and geometric properties of finite non-kissing complexes: we show that their flip graphs are Hasse diagrams of congruence-uniform lattices, and that they can be realized by convex polytopes.
Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.
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