Mod 2 representation of the symmetric group of order 2 over cohomology groups of 2-configuration space of torus

2024/02/17 by Tomoki Tokuda, Tokuda, Tomoki
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric and Algebraic Topology #Mathematics and Applications #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2402.11277

openalex publication_date 2024/02/17 · openalex created_date 2024/02/22 · openalex updated_date 2026/07/28

Abstract

In this article, we compute the mod 2 representarion of the symmetric group of order 2 over the singular cohomology groups of orderd 2-configuration space C₂(T^d) of the d-torus T^d for d≥ 1. As applications of the computation, we determine the Stiefel-Whitney height of C₂(T^d) for any d, and determine \mathbbF₂[Σ₂]-module structure of the cohomology groups of the unordered 2-configuration space of the d-torus for d=2,3 using the Serre spectral sequence.

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