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Intrinsic Transversality Structures
| Content Provider | Semantic Scholar |
|---|---|
| Author | Levitt, Norman |
| Copyright Year | 1987 |
| Abstract | This paper introduces the notion of an intrinsic transversality structure on a Poincare duality space X". Such a space has an intrinsic transversality structure if the embedding of X" into its regular neighborhood W in Euclidean space can be made "Poincare transverse" to a triangulation of W. This notion relates to earlier work concerning transversality structures on spherical fibrations, which are known to be essentially equivalent to topological bundle reductions. Thus, for n > 5, a Poincare duality space X" with a transversality structure on its Spivak normal fibration (i.e., with an "extrinsic" transversality structure) is, up to a surgery obstruction, realizable as a topological manifold. An intrinsic transversality structure, however, not only guarantees the existence of an extrinsic transversality structure but gives rise as well to a canonical solution of the resulting surgery problem. Thus, as our main result, an equivalence is obtained between intrinsic transversality structures and topological manifold structures. This yields a number of corollaries, among which the most important is a "local formula for the total surgery obstruction" which assembles this obstruction to the existence of a manifold structure on X" from the local singularities of a realization of the simple homotopy type of X" as a (non-manifold) simplicial complex. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.maths.ed.ac.uk/~aar/papers/intrins.pdf |
| Alternate Webpage(s) | https://msp.org/pjm/1987/129-1/pjm-v129-n1-p06-s.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Embedding Obstruction Simplicial complex Transversality (mathematics) Transverse wave Turing completeness manifold triangulation |
| Content Type | Text |
| Resource Type | Article |
