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When are two Coxeter orbifolds diffeomorphic?
- Source :
- Michigan Math. J. 63 (2014), 401--421
- Publication Year :
- 2013
-
Abstract
- One can define what it means for a compact manifold with corners to be a "contractible 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.<br />Comment: 24 pages
Details
- Database :
- arXiv
- Journal :
- Michigan Math. J. 63 (2014), 401--421
- Publication Type :
- Report
- Accession number :
- edsarx.1306.6046
- Document Type :
- Working Paper