Dihedral manifold approximate fibrations over the circle

Details Dihedral manifold approximate fibrations over the circle Dihedral manifold approximate fibrations over the circle

2009-03-05

arxiv.org/abs/0903.1094v2

Geometriae Dedicata, Volume 148, Issue 1 (2010), 205-243

Mathematics

Geometric Topology

39 pages

Scientific paper

10.1007/s10711-009-9418-6

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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