Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 8, Number 3 (2008), 1811-1832.
The homology of the stable nonorientable mapping class group
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 (after plus-construction). At odd primes , the –homology coincides with that of , but at the prime 2 the result is less clear. We identify the –homology as a Hopf algebra in terms of the homology of well-known spaces. As an application we tabulate the integral stable homology of 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 consisting of geometrically-defined characteristic classes.
Algebr. Geom. Topol., Volume 8, Number 3 (2008), 1811-1832.
Received: 2 April 2008
Revised: 11 September 2008
Accepted: 12 September 2008
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Randal-Williams, Oscar. The homology of the stable nonorientable mapping class group. Algebr. Geom. Topol. 8 (2008), no. 3, 1811--1832. doi:10.2140/agt.2008.8.1811. https://projecteuclid.org/euclid.agt/1513796908