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2008 The homology of the stable nonorientable mapping class group
Oscar Randal-Williams
Algebr. Geom. Topol. 8(3): 1811-1832 (2008). DOI: 10.2140/agt.2008.8.1811


Combining results of Wahl, Galatius–Madsen–Tillmann–Weiss and Korkmaz, one can identify the homotopy type of the classifying space of the stable nonorientable mapping class group N (after plus-construction). At odd primes p, the Fp–homology coincides with that of Q0(+), but at the prime 2 the result is less clear. We identify the F2–homology as a Hopf algebra in terms of the homology of well-known spaces. As an application we tabulate the integral stable homology of N in degrees up to six.

As in the oriented case, not all of these cohomology classes have a geometric interpretation. We determine a polynomial subalgebra of H(N;F2) consisting of geometrically-defined characteristic classes.


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Oscar Randal-Williams. "The homology of the stable nonorientable mapping class group." Algebr. Geom. Topol. 8 (3) 1811 - 1832, 2008.


Received: 2 April 2008; Revised: 11 September 2008; Accepted: 12 September 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1211.55007
MathSciNet: MR2448874
Digital Object Identifier: 10.2140/agt.2008.8.1811

Primary: 55P47, 57R20
Secondary: 55S12, 55T20

Rights: Copyright © 2008 Mathematical Sciences Publishers


Vol.8 • No. 3 • 2008
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