2017/11/13 by Marcel Bökstedt, Bökstedt, Marcel
Computer Science · Mathematics · #Algebraic Topology (Math.AT) #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #math.CO
paper · pdf · doi:10.48550/arxiv.1711.04624
46 pages
arxiv created 2017/11/13 · openalex publication_date 2017/11/13 · arxiv updated 2017/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate an algebraic problem related to the determination of the fundamental group of a class of spaces of configurations on surfaces. The configuration spaces are spaces of points grouped into colors. Whether two points are allowed to collide is determined by a graph, whose vertices are the colors. In an earlier paper, the fundamental group of such graphs was described as solutions to linear Diophantine equations. In this paper, the problem of describing the set of solution is reformulated using a new type of cohomology groups of graphs. The dependence of the solution on the number of points of each color is studied. The answer is formulated in terms of graph theoretical properties.