Timeline for Homology theory represented by Madsen-Tillmann spectra
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 27, 2014 at 8:17 | comment | added | Oscar Randal-Williams | Very few homotopy groups of $MTO(n)$ or $MTSO(n)$ have been computed. By the description above, the map $s: MTO(n) \to \Sigma^{-n} MO$ induces an isomorphism on homotopy groups is negative degrees, so in this range the groups are known. The homotopy groups of $MTO(n)$ in small positive degrees can be analysed quite effectively by i) computing the cohomology of the homotopy fibre of $s$, ii) running the Adams spectral sequence on it. (All of this can be done for the oriented version too.) For $n=1$ or $2$ I have some charts for the Adams $E^2$ pages of $MTO(n)$ and $MTSO(n)$ on my webpage. | |
| Aug 26, 2014 at 23:37 | comment | added | Alex Turzillo | Have the groups $\pi_k(MTO(n))$ and $\pi_k(MTSO(n))$ been computed? | |
| Aug 26, 2014 at 23:36 | comment | added | Alex Turzillo | Thank you for the detailed response. This is very helpful. | |
| Aug 25, 2014 at 12:41 | history | edited | Oscar Randal-Williams | CC BY-SA 3.0 |
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| Aug 25, 2014 at 9:59 | vote | accept | Alex Turzillo | ||
| Aug 25, 2014 at 9:48 | history | answered | Oscar Randal-Williams | CC BY-SA 3.0 |