Algebraic & Geometric Topology 9 (2009) 2361–2390

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 k ≥ 1, we exhibit lens spaces with an orientation-reversing self-diffeomorphism of order 2^k but no self-map of degree −1 of smaller order.

Keywords

orientation, reversal, oriented, manifold, chiral, chirality, amphicheiral, amphicheirality, achiral, degree

Mathematical Subject Classification

Primary: 55M25

Secondary: 57N65, 57R19, 57S17

References

Publication

Received: 30 July 2009
Revised: 24 September 2009
Accepted: 1 October 2009
Published: 3 November 2009

Authors