Finiteness and Torelli Spaces

Richard Hain

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Finiteness and Torelli Spaces

Richard Hain

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Abstract

Torelli space (in genus g) is the moduli space of compact Riemann surfaces of genus g together with a symplectic basis of their first homology group. It is the quotient of the genus g Teichmuller space by the Torelli group T_g and is a model of the classifying space of T_g. It is known that almost all T_g are not finite complexes. The goal of this note is to present a suite of problems designed to probe the infinite topology of Torelli spaces. Some background is given and a few new results are proved.

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Richard Hain. 2005-08-26. Finiteness and Torelli Spaces. https://arxiv.org/abs/math/0508541

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