Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897584 | Journal of Pure and Applied Algebra | 2018 | 11 Pages |
Abstract
The purpose of this article is to compute the mod 2 cohomology of Îq(K), the mapping class group of the Klein bottle with q marked points. We provide a concrete construction of Eilenberg-MacLane spaces Xq=K(Îq(K),1) and fiber bundles Fq(K)/ΣqâXqâB(Z2ÃO(2)), where Fq(K)/Σq denotes the configuration space of unordered q-tuples of distinct points in K and B(Z2ÃO(2)) is the classifying space of the group Z2ÃO(2). Moreover, we show the mod 2 Serre spectral sequence of the bundle above collapses.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Cristhian E. Hidber, Miguel A. Xicoténcatl,