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Topological Transversality Holds in All Dimensions
| Content Provider | Semantic Scholar |
|---|---|
| Author | Quinn, Francis X. |
| Copyright Year | 2007 |
| Abstract | Moving one submanifold to be transverse to another is a basic and essential operation in the study of manifolds. In the differentiate and PL categories the proof that this operation is always possible is straightforward, and one of the first objectives in developments of the subject. In the topological category it is more difficult; the first progress came in the profound work of Kirby and Siebenmann [4]. Most of what they left unsettled was completed in [7], but a few resistant 4-dimensional cases have remained open. Here we sketch a proof of these exceptional cases; details will appear in Chapter 9 of [3]. We also indicate modifications required in the proof of [4] to reduce the theorem to these cases. In particular this includes the intersection dimension 4 case, which was claimed without proof in [7]. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.ams.org/journals/bull/1988-18-02/S0273-0979-1988-15629-7/S0273-0979-1988-15629-7.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Categories Transversality (mathematics) Transverse wave |
| Content Type | Text |
| Resource Type | Article |
