On generalized configuration space and its homotopy groups

2019/11/05 by Jun Wang, Xuezhi Zhao, Wang, Jun +1
Computer Science · Mathematics · #55Q52 #55R80 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1911.01726

openalex publication_date 2019/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a subset of vector space or projective space. The authors define the generalized configuration space of M which is formed by n-tuples of elements of M where any k elements of each n-tuple are linearly independent. The generalized configuration space gives a generalization of the classical configuration space defined by E.Fadell. Denote the generalized configuration space of M by W_k,n(M). The authors are mainly interested in the calculation about the homotopy groups of generalized configuration space. This article gives the fundamental groups of generalized configuration spaces of ℝP^m for some special cases, and the connections between the homotopy groups of generalized configuration spaces of S^m and the homotopy groups of Stiefel manifolds. It is also proved that the higher homotopy groups of generalized configuration spaces W_k,n(S^m) and W_k,n(ℝP^m) are isomorphic.

Citations

• Non-Reidemeister Knot Theory and Its Applications in Dynamical Systems,\n Geometry, and Topology

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