A local to global argument on low dimensional manifolds
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
For an oriented manifold M whose dimension is less than 4, we use the contractibility of certain complexes associated to its submanifolds to cut M into simpler pieces in order to do local to global arguments. In particular, in these dimensions, we give a different proof of a deep theorem of Thurston in foliation theory that says the natural map between classifying spaces BHomeoδ(M) → BHomeo(M) induces a homology isomorphism where Homeoδ(M) denotes the group of homeomorphisms of M made discrete. Our proof shows that in low dimensions, Thurston’s theorem can be proved without using foliation theory. Finally, we show that this technique gives a new perspective on the homotopy type of homeomorphism groups in low dimensions. In particular, we give a different proof of Hacher’s theorem that the homeomorphism groups of Haken 3-manifolds with boundary are homotopically discrete without using his disjunction techniques.
Originalsprog | Engelsk |
---|---|
Tidsskrift | Transactions of the American Mathematical Society |
Vol/bind | 373 |
Udgave nummer | 2 |
Sider (fra-til) | 1307-1342 |
ISSN | 0002-9947 |
DOI | |
Status | Udgivet - 2020 |
Links
- https://arxiv.org/pdf/1706.04602.pdf
Accepteret manuskript
ID: 270425035