A remark on the homotopy equivalence of SU_n and SL_nC

2010/08/04 by Juan Souto, Souto, Juan · 1 citation
Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.1008.0816

arxiv created 2010/08/04 · openalex publication_date 2010/08/04 · arxiv updated 2010/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Being a maximal compact subgroup of SL_nC, SU_n is a deformation retract of the former group. In this note we prove that, for sufficiently large n, there is no retraction of SL_nC to SU_n which preserves commutativity.

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