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A local to global argument on low dimensional manifolds.
- Source :
-
Transactions of the American Mathematical Society . Feb2020, Vol. 373 Issue 2, p1307-1342. 36p. - Publication Year :
- 2020
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 373
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 141921813
- Full Text :
- https://doi.org/10.1090/tran/7970