Title: When are two Coxeter orbifolds diffeomorphic
Abstract:One can define what it means for a compact manifold with corners to be a manifold with contractible faces. Two combinatorially equivalent, contractible manifolds with contractible faces are diffeomorp...One can define what it means for a compact manifold with corners to be a manifold with contractible faces. Two combinatorially equivalent, contractible manifolds with contractible faces are diffeomorphic if and only if their 4-dimensional faces are diffeomorphic. It follows that two simple convex polytopes are combinatorially equivalent if and only if they are diffeomorphic as manifolds with corners. On the other hand, by a result of Akbulut, for each n > 3, there are smooth, contractible n-manifolds with contractible faces which are combinatorially equivalent but not diffeomorphic. Applications are given to rigidity questions for reflection groups and smooth torus actions.Read More
Publication Year: 2013
Publication Date: 2013-06-25
Language: en
Type: preprint
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Cited By Count: 4
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