Cohomology of the spaces of commuting elements in Lie groups of rank two

2020/10/16 by Masahiro Takeda, Takeda, Masahiro
Mathematics · Medicine · #57T10 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Ophthalmology and Eye Disorders #math.AT #msc:57T10

paper · pdf · doi:10.48550/arxiv.2010.08322

7 pages

arxiv created 2020/10/16 · openalex publication_date 2020/10/16 · arxiv updated 2020/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be the classical group, and let Hom(ℤ^m,G) denote the space of commuting m-tuples in G. Baird proved that the cohomology of Hom(ℤ^m,G) is identified with a certain ring of invariants of the Weyl group of G. In this paper by using the result of Baird we give the cohomology ring of Hom(ℤ²,G) for simple Lie group G of rank 2.

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