2019/04/15 by I. G. Korepanov, Igor G. Korepanov, Korepanov, Igor G.
Mathematics · #12E99 (Secondary) #57Q99 #57R56 #81T70 (Primary) #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.AT #math.QA #msc:12E99 #msc:57Q99 #msc:57R56 #msc:81T70
paper · pdf · doi:10.48550/arxiv.1904.07000
22 pages
arxiv created 2019/04/15 · openalex publication_date 2019/04/15 · arxiv updated 2019/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Hexagon relations are algebraic realizations of four-dimensional Pachner moves. `Constant' -- not depending on a 4-simplex in a triangulation of a 4-manifold -- hexagon relations are proposed, and their polynomial-valued cohomology is constructed. This cohomology yields polynomial mappings defined on the so called `coloring homology space', and these mappings can, in their turn, yield piecewise linear manifold invariants. These mappings are calculated explicitly for some examples. It is also shown that `constant' hexagon relations can be obtained as a limit case of already known `nonconstant' relations, and the way of taking the limit is not unique. This non-uniqueness suggests the existence of an additional structure on the `constant' coloring homology space.