Cohomogeneity one manifolds and selfmaps of nontrivial degree

Details Cohomogeneity one manifolds and selfmaps of nontrivial degree Cohomogeneity one manifolds and selfmaps of nontrivial degree

2007-10-19

arxiv.org/abs/0710.3770v3

Transform. Groups 14 (2009), 225-247

Mathematics

Differential Geometry

v2, v3: minor improvements

Scientific paper

10.1007/s00031-008-9037-6

We construct natural selfmaps of compact cohomgeneity one manifolds with finite Weyl group and compute their degrees and Lefschetz numbers. On manifolds with simple cohomology rings this yields in certain cases relations between the order of the Weyl group and the Euler characteristic of a principal orbit. We apply our construction to the compact Lie group SU(3) where we extend identity and transposition to an infinite family of selfmaps of every odd degree. The compositions of these selfmaps with the power maps realize all possible degrees of selfmaps of SU(3).

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