arXiv subjects

Carl-Friedrich Bödigheimer

Publications and source records attributed to Carl-Friedrich Bödigheimer.

2 recordsLinked to original sources

arXiv2022

Computations in the unstable homology of moduli spaces of Riemann surfaces

In this article we give a survey of homology computations for moduli spaces $\mathfrak{M}_{g,1}^m$ of Riemann surfaces with genus $g\geqslant 0$, one boundary curve, and $m\geqslant 0$ punctures. While rationally and stably this question has a satisfying answer by the Madsen-Weiss theorem, the unstable homology remains notoriously complicated. We discuss calculations with integral, mod-2, and rational coefficients. Furthermore, we determine, in most cases, explicit generators using homology operations.

math.AT↗

arXiv2012

Embeddings of braid groups into mapping class groups and their homology

We construct several families of embeddings of braid groups into mapping class groups of orientable and non-orientable surfaces and prove that they induce the trivial map in stable homology in the orientable case, but not so in the non-orientable case. We show that these embeddings are non-geometric in the sense that the standard generators of the braid group are not mapped to Dehn twists.

math.AT↗