Volume 8, issue 3 (2008)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21, 1 issue

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
The homology of the stable nonorientable mapping class group

Oscar Randal-Williams

Algebraic & Geometric Topology 8 (2008) 1811–1832

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.

mapping class group, characteristic class, surface bundle, nonorientable surface, Dyer–Lashof operation, Eilenberg–Moore spectral sequence
Mathematical Subject Classification 2000
Primary: 57R20, 55P47
Secondary: 55S12, 55T20
Received: 2 April 2008
Revised: 11 September 2008
Accepted: 12 September 2008
Published: 20 October 2008
Oscar Randal-Williams
Mathematical Institute
24–29 St Giles’