On the Cohomology of the Total Space of Classifying Space for Commutativity in U(3)

2021/06/17 by Santanil Jana, Jana, Santanil
Mathematics · Medicine · #55R20 #55R40 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders

paper · pdf · doi:10.48550/arxiv.2106.09195

openalex publication_date 2021/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we describe the total space E_com U(3) of the principal U(3)-bundle associated with the classifying space for commutativity B_com U(3) as a homotopy colimit of a diagram of spaces and offer a computation of the mod 2 and mod 3 cohomologies of E_com U(3) by utilizing the spectral sequence associated with a homotopy colimit. We investigate the cohomology of different spaces in the homotopy colimit diagram. These spaces are intriguing in their own right and contribute to the overall fascination of the analysis. We also present the ring structure of the rational cohomology of E_com U(3).

Related

• The classifying space for commutativity of geometric orientable 3-manifold groups
• Cohomology of classifying spaces of rank 3 Kac-Moody groups
• Rational SU(3)-equivariant cohomology theories
• Characteristic classes for TC structures
• The Complex of Affinely Commutative Sets