2011/08/24 by Nikolai Mnëv, Mnev, Nikolai
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1108.4733
openalex publication_date 2011/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Here we are fixing an output of a trivial calculation based on Konsevich's differential 2-form for the Chern class of polygon bundle. As a result an interesting combinatorics and arithmetics jumps right out of a jukebox. The calculation gives very simple rational combinatorial characteristics (we call it "curvature") of a triangulated S1 bundle over a 2-simplex, which is a local combinatorial formula for the first Chern class. The curvature is expressed in terms of cyclic word in 3-character alphabet associated to the bundle. From the point of view of simplicial combinatorics the word is a canonical shelling of the total complex. If you know a triangulation of a bundle - you can really easily compute the Chern class.