A remark on the homotopy equivalence of SU_n and SL_nC

Details A remark on the homotopy equivalence of SU_n and SL_nC A remark on the homotopy equivalence of SU_n and SL_nC

2010-08-04

arxiv.org/abs/1008.0816v1

Mathematics

Algebraic Topology

Scientific paper

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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