Homological stability for the mapping class groups of non-orientable surfaces

Details Homological stability for the mapping class groups of non-orientable surfaces Homological stability for the mapping class groups of non-orientable surfaces

2006-01-13

arxiv.org/abs/math/0601310v2

Invent. math. 171 (2008), 389-424.

Mathematics

Geometric Topology

Scientific paper

10.1007/s00222-007-0085-7

We prove that the homology of the mapping class groups of non-orientable surfaces stabilizes with the genus of the surface. Combining our result with recent work of Madsen and Weiss, we obtain that the classifying space of the stable mapping class group of non-orientable surfaces, up to homology isomorphism, is the infinite loop space of a Thom spectrum build from the canonical bundle over the Grassmannians of 2-planes in R^{n+2}. In particular, we show that the stable rational cohomology is a polynomial algebra on generators in degrees 4i--this is the non-oriented analogue of the Mumford conjecture.

Affiliated with

Also associated with

No associations

Rating

Homological stability for the mapping class groups of non-orientable surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Homological stability for the mapping class groups of non-orientable surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Homological stability for the mapping class groups of non-orientable surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-452349