Dihedral manifold approximate fibrations over the circle

Bruce Hughes; Qayum Khan

doi:10.1007/s10711-009-9418-6

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arXiv · 0903.1094

Dihedral manifold approximate fibrations over the circle

Bruce Hughes·Qayum Khan

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Abstract

Consider the cyclic group C_2 of order two acting by complex-conjugation on the unit circle S^1. The main result is that a finitely dominated manifold W of dimension > 4 admits a cocompact, free, discontinuous action by the infinite dihedral group D_\infty if and only if W is the infinite cyclic cover of a free C_2-manifold M such that M admits a C_2-equivariant manifold approximate fibration to S^1. The novelty in this setting is the existence of codimension-one, invariant submanifolds of M and W. Along the way, we develop an equivariant sucking principle for certain orthogonal actions of finite groups on Euclidean space.

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Bruce Hughes, Qayum Khan. 2009-03-05. Dihedral manifold approximate fibrations over the circle. https://doi.org/10.1007/s10711-009-9418-6

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