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Finiteness and Torelli Spaces

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arxiv math/0508541 v1 pith:D23P6X5R submitted 2005-08-26 math.GT math.AG

Richard Hain This is my paper · ORCID
classification math.GTmath.AG
keywords spacetorelligenusgroupspacesalmostbackgroundbasis
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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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Cited by 1 Pith paper

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  1. Finite generation, algebraicity, and representation stability for homology of Torelli groups

    math.GT 2026-06 unverdicted novelty 8.0 of 10

    Proves finite generation of H_k(I_g; Z) for k ≤ g-2 and that rational homology is an algebraic Sp(2g,Z)-representation, turning conditional cohomology computations into theorems and proving Morita's conjecture.

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