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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Approximation by equivariant homeomorphisms. I


Authors: Mark Steinberger and James West
Journal: Trans. Amer. Math. Soc. 302 (1987), 297-317
MSC: Primary 57S17; Secondary 57N30, 57Q10, 57Q55, 57R80
MathSciNet review: 887511
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Abstract: Locally linear (= locally smoothable) actions of finite groups on finite dimensional manifolds are considered in which two incident components of fixed point sets of subgroups either coincide or one has codimension at least three in the other. For these actions, an equivariant $ \alpha $-approximation theorem is proved using engulfing techniques. As corollaries are obtained equivariant "fibrations are bundles" and "controlled $ h$-cobordism" theorems, as well as an equivariant version of Edwards' cell-like mapping theorem and the vanishing of the set of transfer-invariant $ G$-homotopy topological structures, rel boundary, on $ {T^n} \times {D_\rho }$ (when $ {T^n}$ is the $ n$-torus with trivial $ G$ action and $ {D_\rho }$ is a representation disc).


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0887511-8
PII: S 0002-9947(1987)0887511-8
Article copyright: © Copyright 1987 American Mathematical Society