A remark on the homotopy equivalence of SU_n and SL_nC
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commutativitycompactdeformationequivalenceformergrouphomotopylarge
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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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