Timeline for Stable moduli interpretation of $\mathbb{R}\mathrm{P}^\infty_{-1}$
Current License: CC BY-SA 3.0
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| Aug 22, 2015 at 13:57 | comment | added | user51223 | If this still counts important, by work of Wahl an analogous result of Madsen-Wiess holds in unoriented case: Let $MTO(2)=:BO(2)^{-\gamma_2}$ with $\gamma_2\to BO(2)$ being the canonicla bundle. Then the moduli $\mathcal{N}_\infty$ for unoriented surfaces is homotopy equivalent to $\Omega^\infty MTO(2)$. Now, $\mathbb{R} P_{-1}$ is related to this by a cofibration of spectra $$MTO(2)\to BO(2)_+\to\mathbb{R} P_{-1}$$ which lead to a fibration of infinite loop spaces $$\Omega^\infty MTO(2)\to QBO(2)_+\to \Omega^\infty\mathbb{R}P_{-1}.$$ Found this when searching for `root invariant'. | |
| Jan 29, 2014 at 10:29 | history | edited | Neil Strickland | CC BY-SA 3.0 |
added 136 characters in body
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| Jan 29, 2014 at 10:14 | history | answered | Neil Strickland | CC BY-SA 3.0 |