Wiedersehen metrics and exotic involutions of Euclidean spheres

Details Wiedersehen metrics and exotic involutions of Euclidean spheres Wiedersehen metrics and exotic involutions of Euclidean spheres

2005-01-06

arxiv.org/abs/math/0501091v2

Mathematics

Geometric Topology

17 pages, 5 figures, a QuickTime movie visualizing an exotic involution of S^5 is currently available at http://www.ruhr-uni

Scientific paper

We provide explicit, simple, geometric formulas for free involutions rho of Euclidean spheres that are not conjugate to the antipodal involution. Therefore the quotient S^n/rho is a manifold that is homotopically equivalent but not diffeomorphic to RP^n. We use these formulas for constructing explicit non-trivial elements in pi_1 Diff(S^5) and pi_1 Diff(S^13) and to provide explicit formulas for non-cancellation phenomena in group actions.

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