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International Seminar for Young Researchers "Algebraic, Combinatorial and Toric Topology"
December 17, 2020 16:05–16:45, online
 


On the structure of the top homology group of the Johnson kernel

I. A. Spiridonov

National Research University "Higher School of Economics", Moscow
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Abstract: The Johnson kernel of a genus $g$ oriented surface $\Sigma_{g}$ is a subgroup $\mathcal{K}(\Sigma_{g})$ of the mapping class group $\mathrm{Mod}(\Sigma_{g})$ generated by all Dehn twists along separating curves. Given a family of $2g-3$ pairwise disjoint separating curves on $\Sigma_{g}$ one can construct the corresponding abelian cycle in the top homology group $H_{2g-3}(\mathcal{K}(\Sigma_{g}), \mathbb{Z})$; such abelian cycles we call primitive. We will discuss the structure of the subgroup of $H_{2g-3}(\mathcal{K}(\Sigma_{g}), \mathbb{Z})$ generated by all primitive abelian cycles. In particular, we will describe the relations between them.

Language: English

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