#### Volume 9, issue 4 (2009)

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Orientation reversal of manifolds

### Daniel Müllner

Algebraic & Geometric Topology 9 (2009) 2361–2390
##### 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 $\ge 3$. We also produce simply-connected, strongly chiral manifolds in every dimension $\ge 7$. For every $k\ge 1$, 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 2000
Primary: 55M25
Secondary: 57S17, 57N65, 57R19