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19 votes
4 answers
2k views

Details for the action of the braid group B_3 on modular forms

I'm reading Terry Gannon's Moonshine Beyond the Monster, and in section 2.4.3 he hints at (but does not explicitly describe) a way to extend the action of $SL_2(\mathbb{Z})$ on modular forms to an ...
Qiaochu Yuan's user avatar
22 votes
4 answers
3k views

Betti numbers of moduli spaces of smooth Riemann surfaces

Where can I find a list of the known Betti numbers of the moduli spaces $\mathcal{M}_{g,n}$ of genus $g$ Riemann surfaces with $n$ marked points? I need it to cross check results by an implemented ...
domenico fiorenza's user avatar
15 votes
3 answers
1k views

Are there graph models for other moduli spaces?

Recall that a ribbon graph is a graph with a cyclic ordering at each vertex and such that each vertex has valence greater than or equal to 3. This cyclic ordering exactly gives one the information to ...
skupers's user avatar
  • 8,167
2 votes
1 answer
1k views

Moduli space of flat connections over a torus

Let us fix a principal bundle $G\hookrightarrow P\to T^{2}$, where $T^{2}$ is a torus. Is the moduli space of flat connections on $P$ known? At least, it is known for some particular gauge groups, ...
Bilateral's user avatar
  • 2,816