Abstract
We study decorated mapping class groups, i.e., mapping class groups of surfaces with marked points and boundary components, and their behaviour under stabilization maps with respect to the genus, the number of punctures and boundary components. Decorated mapping class groups are non-trivial extensions of the undecorated mapping class group, and the first result states that the extension is homologically trivial when one stabilizes with respect to the genus. The second result implies that one also gets splittings of homology groups when stabilizing with respect to the number of punctures and boundary components.
Supported by an Advanced Fellowship of the EPSRC.
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Bödigheimer, CF., Tillmann, U. (2001). Stripping and splitting decorated mapping class groups. In: Aguadé, J., Broto, C., Casacuberta, C. (eds) Cohomological Methods in Homotopy Theory. Progress in Mathematics, vol 196. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8312-2_6
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DOI: https://doi.org/10.1007/978-3-0348-8312-2_6
Publisher Name: Birkhäuser, Basel
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