Work

Realizing regular representations of finite groups

Year: 2024

Type: article

Abstract: Given a regular representation of a finite group G and a positive integer number n , we construct a (finite) topological space X such that its group of homotopy classes of self-homotopy equivalences ℰ ⁡ ( 𝑋 ) and its group of homeomorphisms 𝐴 ⁢ 𝑢 ⁢ 𝑡 ⁡ ( 𝑋 ) are isomorphic to G , and the action of G on the n -th homology group 𝐻 𝑛 ⁡ ( 𝑋 ) is the regular representation. We also discuss other representations.

Source: Journal of Algebra

DOI: 10.1016/j.jalgebra.2024.09.016

Author: Pedro J. Chocano

Institution: Universidad Rey Juan Carlos

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,140

Funder: Ministerio de Ciencia, Innovación y Universidades