Timeline for Cobordism categories that don't involve manifolds
Current License: CC BY-SA 2.5
5 events
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| Dec 16, 2022 at 14:32 | comment | added | Greg Friedman | Here's the actual reference to the Pardon paper: Pardon, William L. Intersection homology Poincaré spaces and the characteristic variety theorem. Comment. Math. Helv. 65 (1990), no. 2, 198–233. and here's the Siegel paper: Siegel, P. H. Witt spaces: a geometric cycle theory for KO-homology at odd primes. Amer. J. Math. 105 (1983), no. 5, 1067–1105. | |
| Dec 15, 2022 at 12:47 | comment | added | The Amplitwist |
The link to springerlink.com is broken. I'm also unable to find any snapshot saved on the Wayback Machine.
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| Mar 30, 2011 at 23:37 | comment | added | Greg Friedman | Well, I don't think you need to consider free abelian groups directly. The elements of the $n$th Witt bordism group of $X$ are equivalence classes of maps $f:W\to X$ of $n$-dimensional Witt spaces to $X$. Two, say $f_1, f_2: W_1, W_2\to X$ are equivalent if there is an $n+1$ dimensional Witt space with boundary $U$ and a map $F:U\to X$ that restricts to $f_1$ and $f_2$ (with appropriate signs) on the boundary. Then the addition is just disjoint union of spaces and maps, i.e. $f_1+f_2$ is $f_1\amalg f_2: W_1\amalg W_2\to X$. So you don't need to form a free abelian group on generators for this. | |
| Mar 28, 2011 at 22:31 | comment | added | Sean Tilson | so this is a geometric model like the "model" of $MU_*X$ where you take manifolds with maps to $X$ and look at the free abelian group modulo cobordisms? (Maybe I mean $MU^*X$) | |
| Mar 28, 2011 at 21:08 | history | answered | Greg Friedman | CC BY-SA 2.5 |