Timeline for Adams Spectral sequence and Pontrjagin-Thom construction [Reference request]
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jan 17, 2018 at 6:40 | comment | added | user51223 | @RobertBruner Thanks for the reference. I thought that there is no discussion of this in the literature and just believed to be true as the arguments seemed ``standard'' ! | |
| Jan 17, 2018 at 0:09 | comment | added | Robert Bruner | I discuss this as well as `higher products' in MR1831346 Bruner, Robert R. Extended powers of manifolds and the Adams spectral sequence. Homotopy methods in algebraic topology (Boulder, CO, 1999), 41--51, Contemp. Math., 271, Amer. Math. Soc., Providence, RI, 2001. | |
| Aug 18, 2015 at 8:34 | comment | added | user51223 | @43326 I think somehow it takes the statements for granted. I suppose the underlying discussions on Bord in that discussion has to arise from the known facts on the sphere spectrum or have I understood the discussions within there incorrectly?! Still, it was an interesting one. Thank you! Let me add that my main concern in looking for such a proof is that I feel there is are differential geometry technicalities within such proofs which the natural approach suggested by Ryan has to go through them! | |
| Aug 17, 2015 at 16:21 | comment | added | user43326 | I don't know if this helps you to find a published reference, but the post mathoverflow.net/questions/173691/… deals with the second question. | |
| Aug 15, 2015 at 7:02 | comment | added | user51223 | @MingcongZeng Yes, it seems it is! Thanks. | |
| Aug 15, 2015 at 6:59 | comment | added | user51223 | @RyanBudney Thanks. I also thought of this, but it seems it has not been written down anywhere. I wonder what did you think of the case of other bordism theories? | |
| Aug 15, 2015 at 4:47 | comment | added | Mingcong Zeng | The first statement may be 2.3.3 in Ravenel's complex cobordism book. | |
| Aug 14, 2015 at 22:16 | comment | added | Ryan Budney | If you take the multiplication on framed cobordism to be the product of framed manifolds, and the multiplication on stable homotopy of spheres to be the smash product of maps, then yes its multiplicative. It's a direct argument with little fuss, provided your input maps are transverse to begin with. So it generalizes to other bordism theories. I haven't thought about the Adams Spectral Sequence since grad school so I'll leave that to others. | |
| Aug 14, 2015 at 21:27 | history | asked | user51223 | CC BY-SA 3.0 |