Timeline for Configuration spaces and non homeomorphic vector bundles
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Mar 29, 2022 at 2:02 | comment | added | David Roberts♦ | The link in Ryan's comment is broken, here's a replacement: arxiv.org/abs/math/0401075. | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Feb 5, 2014 at 3:56 | history | edited | Ricardo Andrade | CC BY-SA 3.0 |
replaced deprecated tag 'topology'; added tag; replaced expression 'homotopic'
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| Mar 29, 2012 at 11:27 | vote | accept | alvarezpaiva | ||
| Mar 29, 2012 at 8:28 | answer | added | Paolo Salvatore | timeline score: 16 | |
| Mar 28, 2012 at 15:39 | comment | added | Mark Grant | @Ben: I believe the case of simply-connected and two points is also still open. | |
| Mar 28, 2012 at 8:34 | comment | added | alvarezpaiva | @Misha: Yes, this solves the first problem. This was the gist of Goodwillie's answer to zygund's question. I'm just a bit curious as to Wu Wen-Tsün's observation and would like to know how much topological, but non-homotopical, information can be encoded in configuration spaces. By the remarks of Ryan and Ben it seems quite a bit is known about this question. | |
| Mar 28, 2012 at 0:52 | comment | added | Ryan Budney | @Ben, right, but simply-connected 4-manifolds are still below the (known) threshold for the homotopy-type of configuration spaces to be a homotopy-invariant of the input manifold. | |
| Mar 28, 2012 at 0:14 | answer | added | Ryan Budney | timeline score: 3 | |
| Mar 27, 2012 at 22:53 | comment | added | Ben Wieland | I think some context is needed for the Salvatore-Longoni paper. For compact manifolds, the homotopy type of configuration spaces are homotopy invariants if the manifolds are highly connected and the number of points is small (open: just simply connected + many points), but S&L give a counterexample when the compact manifolds have fundamental group. | |
| Mar 27, 2012 at 21:15 | comment | added | Misha | Look at the intersection pairing on $H_2$ of the total space. From this you can read off the Euler number and, hence, the Chern class. | |
| Mar 27, 2012 at 20:15 | comment | added | Ryan Budney | Have you read the Salvatore-Longoni paper? front.math.ucdavis.edu/0401.5075 It's very close in spirit with your line of inquiry. | |
| Mar 27, 2012 at 19:58 | history | edited | alvarezpaiva | CC BY-SA 3.0 |
deleted 4 characters in body
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| Mar 27, 2012 at 19:49 | history | asked | alvarezpaiva | CC BY-SA 3.0 |