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Results tagged with mapping-class-groups
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user 318
Topology of groups of automorphisms of surfaces, and high dimensional analogues.
7
votes
Extension of the group $Sp(2g,\mathbb{Z})$
For $g \geq 3$, the map
$$H^*(Sp(2g,\mathbb{Z});\mathbb{Z}) \longrightarrow H^*(M_g;\mathbb{Z})$$
is known to be an isomorphism for $* \leq 2$. In particular, by universal coefficients the map
$$H^2(S …
- 18.2k
6
votes
Is there Harer stability for moduli of curves with level structure?
This is not an answer to your question, but is directly related to your remark so I thought I should mention it.
I have recently proved, though I am afraid that it has not appeared yet, that moduli s …
- 18.2k
2
votes
Mappings of mapping class groups
The second of your questions is answered in
Graham Hope and Ulrike Tillmann "On the Farrell cohomology of the mapping class group of non-orientable surfaces" Proc. Amer. Math. Soc. 137 (2009), no. 1, …
- 18.2k
4
votes
Accepted
Elements of infinite order in the topological mapping class group
Let me suppose that $M$ is a closed manifold of dimension $d$, and let $\varphi : M \to M$ be a diffeomorphism / homeomorphism which is homotopic to the identity, and choose such a homotopy $h_t$. The …
- 18.2k
2
votes
Accepted
Homology dimension of the mapping class group of a surface with boundary
There is a fibration sequence
$$\mathbb{S}(\Sigma_g) \to \mathcal{M}_{g}^1 \to \mathcal{M}_g$$
where $\mathcal{M}_g$ is the moduli space of Riemann surfaces, $\mathcal{M}_{g}^1$ is the moduli space of …
- 18.2k
2
votes
Euler class of vertical tangent bundle of the surface bundle over circle
Let me not Poincare dualise, and work in cohomology.
Let me generalise the setting you have described, and consider the universal surface bundle $\pi : E \to M_g^1$ over the moduli space of surfaces w …
- 18.2k