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arXiv · 0907.5283

Orientation reversal of manifolds

Daniel Müllner
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Abstract

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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Daniel Müllner. 2010-12-17. Orientation reversal of manifolds. https://doi.org/10.2140/agt.2009.9.2361

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