2015/09/21 by J. Y. Li, Li, J. Y., V. V. Vershinin +4
Computer Science · Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #msc:18G30 #msc:55U10
paper · pdf · doi:10.48550/arxiv.1509.06424
19 pages
arxiv created 2015/09/21 · arxiv updated 2015/09/23
Let A be either a simplicial complex K or a small category \mathcal C with V(A) as its set of vertices or objects. We define a twisted structure on A with coefficients in a simplicial group G as a function δ\colon V(A)\longrightarrow End(G), v↦ δv such that δv∘ δw=δw∘ δv if there exists an edge in A joining v with w or an arrow either from v to w or from w to v. We give a canonical construction of twisted simplicial group as well as twisted homology for A with a given twisted structure. Also we determine the homotopy type of of this simplicial group as the loop space over certain twisted smash product.