A remark on the homotopy equivalence of SU_n and SL_nC

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.

Cited by in corpus (1)

• Topology of character varieties of Abelian groups