Timeline for Is there a connection between the theory of motives and homotopy theory?
Current License: CC BY-SA 2.5
10 events
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| Feb 18, 2011 at 7:08 | comment | added | Sean Tilson | Oh, and the relevant homology theories do not apply to topological spaces or CW complexes, they are of varieties. This really is a sort of apples and oranges thing. Interesting nonetheless. | |
| Feb 18, 2011 at 7:07 | comment | added | Sean Tilson | So you are asking if their is a theory of motives of topological spaces? or CW complexes? or spectra? I think that is a very different issue then what motivic homotopy theory deals with. Motivic homotopy theory is about homotopy theory of schemes. It also does not provide a category of (mixed) motives that Weil was interested in having produced. | |
| Feb 18, 2011 at 2:08 | comment | added | Aaron Mazel-Gee | Right -- of course I was being pretty vague. I'm only idly speculating, but I'd imagine that the notion of spectrum originally arose from the Freudenthal suspension theorem? And/or maybe from the fact that $\Omega K(G,n)=K(G,n-1)$. | |
| Feb 17, 2011 at 22:40 | comment | added | David Roberts♦ | @Aaron - I disagree that a spectrum is "the" homotopy theoretic generalisation of a topological space. It is only a stable homotopy theoretic generalisation of a topological space. Or rather, that a topological space gives rise to a rather special example of a spectrum. | |
| Feb 17, 2011 at 20:32 | answer | added | Beren Sanders | timeline score: 9 | |
| Feb 14, 2011 at 10:16 | comment | added | Konrad Voelkel | You said you've read that "motives were designed to be the common part of the many homology theories", but I think that's not quite correct: motives are designed to contain the (co)homological information of algebraic objects (schemes, varieties). I guess there are a lot of "ill-behaved" topological spaces which don't have the homotopy type of a CW-complex and don't have anything to do with algebraic geometry, where motivic ideas don't apply. On the other hand, if anyone knows of a theory of motives for arbitrary topological spaces, I'd be interested :-) | |
| Feb 14, 2011 at 9:58 | comment | added | Fernando Muro | You say there's only one homotopy theory... but there are tons!! | |
| Feb 14, 2011 at 9:34 | comment | added | Aaron Mazel-Gee | I certainly couldn't claim to fully understand this paper, but I can tell you that a "spectrum" is the homotopy-theoretic generalization of a topological space and that this paper talks about motivic spectra whole lot: arxiv.org/abs/0712.2817 | |
| Feb 14, 2011 at 8:55 | comment | added | Thomas Riepe | An MFO report: mfo.de/programme/schedule/2010/20/OWR_2010_23.pdf | |
| Feb 14, 2011 at 7:22 | history | asked | teil | CC BY-SA 2.5 |