Abstract: We discuss a functor that produces 'topological field theories' from representations of infinite symmetric group. A "topological field theory" is a functor from a category of bodisms to a category of linear spaces and linear operators. Here we discuss bordisms of two-dimensional simplicial surfaces equipped with additional data (a coloring). Gluing of surfaces along boundary corresponds to multiplication of operators. The construction is simple and is based on multiplication of double cosets in the spirit of Ismagilov and Olshanski (it is a strangre 'ergodic' operation on infinite-dimensional groups replacing the usual convolution).