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2009 Orientation reversal of manifolds
Daniel Müllner
Algebr. Geom. Topol. 9(4): 2361-2390 (2009). DOI: 10.2140/agt.2009.9.2361

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 3. We also produce simply-connected, strongly chiral manifolds in every dimension 7. For every k1, we exhibit lens spaces with an orientation-reversing self-diffeomorphism of order 2k but no self-map of degree 1 of smaller order.

Citation

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Daniel Müllner. "Orientation reversal of manifolds." Algebr. Geom. Topol. 9 (4) 2361 - 2390, 2009. https://doi.org/10.2140/agt.2009.9.2361

Information

Received: 30 July 2009; Revised: 24 September 2009; Accepted: 1 October 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1284.57027
MathSciNet: MR2558314
Digital Object Identifier: 10.2140/agt.2009.9.2361

Subjects:
Primary: 55M25
Secondary: 57N65, 57R19, 57S17

Rights: Copyright © 2009 Mathematical Sciences Publishers

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Vol.9 • No. 4 • 2009
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