Timeline for Non-additive cohomology theories induced by arbitrary prespectra
Current License: CC BY-SA 4.0
6 events
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| Oct 11 at 2:07 | comment | added | Jonathan Beardsley | This is only tangentially related, but if you work with Segal's Gamma space approach to spectra then the inclusion Gamma^op→Set_* is often called the sphere spectrum. It's not, of course, because it's not fibrant in the stable model structure. It's not a "spectrum" at all. But its underlying space is indeed S⁰ and it has the simplicial circle as its delooping. This object is what Connes and Consani call F_1. The homology theory it induces, in the sense of Bousfield and Friedlander, is "the identity," basically. | |
| Sep 19 at 17:29 | comment | added | Connor Malin | You just are using different gradings. | |
| Sep 19 at 16:12 | history | edited | Perry Hart |
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| Sep 19 at 15:23 | comment | added | Perry Hart | @ConnorMalin Are you referring to Proposition 2.8 in the Blue Book? If so, then the difference in indexing makes me think we want $F$ to be an $\Omega$-spectrum so that the two colimit formulas align up to a degree shift. What am I missing? | |
| Sep 19 at 11:03 | comment | added | Connor Malin | So the formula that you give is already a method to derive the mapping set between a finite CW complex $X$ and a prespectrum $F$ and is essentially the method Adams uses in his "Blue Book". In particular, we don't actually need $F$ to be an $\Omega$-spectrum to get the correct value. | |
| Sep 19 at 4:48 | history | asked | Perry Hart | CC BY-SA 4.0 |