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Given a concrete category C, with objects denoted Obj(C), and an equivalence relation ~ on Obj(C) given by morphisms in C. The moduli set for Obj(C) is the set of equivalence classes with respect to ~; denoted Iso(C). When Iso(C) is an object in the category Top, then the moduli set is called a moduli space.

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Tabulation of known unstable rational homology of moduli space?

Does there exist a tabulation of the known rational homology of mapping class groups of genus $g$ with $m$ punctures? I'm most interested in the case when punctures can be permuted.
Jim Conant's user avatar
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12 votes

Are there graph models for other moduli spaces?

Outer automorphisms of free groups have a rational classifying space given by metric graphs, called "outer space," first described in a paper by Culler and Vogtmann. The rational cohomology of Out$(F …
Jim Conant's user avatar
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