2018/08/26 by Igor G. Korepanov, Korepanov, Igor G.
Mathematics · #12E99 (Secondary) #57Q99 #57R56 #81T70 (Primary) #Algebraic Topology (math.AT) #FOS: Mathematics #Quantum Algebra (math.QA) #math.AT #math.QA #msc:12E99 #msc:57Q99 #msc:57R56 #msc:81T70
paper · pdf · doi:10.48550/arxiv.1808.10723
9 pages
arxiv created 2018/08/26 · arxiv updated 2018/09/03
Hexagon relations are algebraic realizations of four-dimensional Pachner moves, and there are hexagon relations admitting nontrivial cohomologies and leading thus to piecewise linear (PL) 4-manifold invariants. We show that some - but not all! - of the known nontrivial cohomologies can be obtained from a single integral bilinear form corresponding to a PL 4-manifold by using a Frobenius homomorphism for a half of `color' variables (or different Frobenius homomorphisms for both halves). This form can be regarded as a sophisticated analogue of the manifold's intersection form.