Orientation reversal of manifolds

Details Orientation reversal of manifolds Orientation reversal of manifolds

2009-07-30

arxiv.org/abs/0907.5283v2

Algebraic & Geometric Topology 9 (2009) 2361-2390

Mathematics

Geometric Topology

This is the update to the final version. 22 pages

Scientific paper

10.2140/agt.2009.9.2361

We call a closed, connected, orientable manifold in one of the categories TOP, PL or DIFF chiral if it does not admit an orientation-reversing automorphism and amphicheiral otherwise. Moreover, we call a manifold strongly chiral if it does not admit a self-map of degree -1. We prove that there are strongly chiral, smooth manifolds in every oriented bordism class in every dimension greater than two. We also produce simply-connected, strongly chiral manifolds in every dimension greater than six. For every positive integer k, we exhibit lens spaces with an orientation-reversing self-diffeomorphism of order 2^k but no self-map of degree -1 of smaller order.

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