Equivariant Embeddings in Euclidean Space

The purpose of this paper is to prove equivariant versions of some basic theorems in differential topology for proper Lie group actions. In particular, we study how to extend equivariant isotopies and then apply these results to obtain equivariant smoothing and gluing theorems. We also study equivariant collars and tubular neighbourhoods. When possible, we follow the ideas in the well-known book of M W Hirsch. When necessary, we use results from the differential topology of Hilbert spaces. 57S20

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“…There are at least two methods for doing this. One is to use a theorem of Mostow [16] to Q-equivariantly embed Y in a linear representation of Q on some Euclidean space R n . (A proof of Mostow's Theorem can be found in [3, pp.…”

Section: The First Class Of Examplesmentioning

confidence: 99%

Some Examples of Discrete Group Actions on Aspherical Manifolds

Davis

Leary

2003

High-Dimensional Manifold Topology

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Abstract. We construct two classes of examples of a virtually torsionfree group G acting properly and cocompactly on a contractible manifold X. In the first class of examples the universal space for proper actions, EG, has no model with finitely many orbits of cells. The reason is that the centralizers of certain finite subgroups of G will not have finitetype classifying spaces. In the second class of examples X is a CAT (0) manifold upon which G acts by isometries. It follows that X is a model for EG. In these examples the fixed point sets of certain finite subgroups of G are not manifolds and the centralizers of these subgroups are not virtual Poincaré duality groups.

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Equivariant Embeddings in Euclidean Space

Cited by 179 publications

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Transformation groups on a homological manifold

Transformation groups on a homological manifold

Equivariant collaring, tubular neighbourhood and gluing theorems for proper Lie group actions

Some Examples of Discrete Group Actions on Aspherical Manifolds

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