Cohomogeneity One Manifolds and Selfmaps of Nontrivial Degree
نویسنده
چکیده
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 realize all possible degrees by explicit polynomial selfmaps.
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