2008/09/24 by Rinat Kashaev, Kashaev, Rinat, I. G. Korepanov +4 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math-ph #math.AT #math.GT #math.MP #msc:57M27 #msc:57Q99
paper · pdf · doi:10.48550/arxiv.0809.4239
23 pages, 2 figures, 1 table
arxiv created 2008/09/24 · arxiv updated 2009/12/01
In this paper, we begin constructing a new finite-dimensional topological quantum field theory (TQFT) for three-manifolds, based on group PSL(2,C) and its action on a complex variable by fractional-linear transformations, by providing its key ingredient -- a new type of chain complexes. As these complexes happen to be acyclic often enough, we make use of their torsion to construct different versions of manifold invariants. In particular, we show how to construct a large set of invariants for a manifold with boundary, analogous to the set of invariants based on Euclidean geometric values and used in a paper by one of the authors for constructing a "Euclidean" TQFT. We show on examples that our invariants are highly nontrivial.