Timeline for Are non-PL manifolds CW-complexes?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Sep 3, 2013 at 15:47 | comment | added | hsp | Hatcher's Algebraic Topology p. 529 has a paragraph answering this question very clearly for compact manifolds (not including results in 2013 of course). However his references are to two long dense books, without page specification. | |
| May 1, 2013 at 16:10 | comment | added | Lee Mosher | Update: recent work of Davis, Fowler, and Lafont front.math.ucdavis.edu/1304.3730 shows that in every dimension ≥6 there exists a closed aspherical manifold that is not homeomorphic to a simplicial complex. | |
| Aug 27, 2010 at 4:50 | comment | added | algori | It turns out that my first comment was a bit wrong. Here are the slides of A. Ranicki's talk in Orsay. www.maths.ed.ac.uk/~aar/slides/orsay.pdf It says on p. 5 there that a compact manifold of dimension other than 4 is a CW complex. There is a related conjecture that says that each closed manifold of dimension $\geq 5$ is homeomorphic to a polyhedron (there are 4-manifolds for which this is false). See arxiv.org/pdf/math/0212297. I'm not sure what if anything is known about the noncompact case. | |
| Aug 27, 2010 at 4:48 | comment | added | A grad student | @algori : I thought you had posted an (important sounding) comment? Why did you delete it? | |
| Aug 27, 2010 at 4:04 | answer | added | Ryan Budney | timeline score: 15 | |
| Aug 27, 2010 at 3:53 | answer | added | Mariano Suárez-Álvarez | timeline score: 7 | |
| Aug 27, 2010 at 3:48 | history | asked | A grad student | CC BY-SA 2.5 |