Finiteness and Torelli Spaces

Details Finiteness and Torelli Spaces Finiteness and Torelli Spaces

2005-08-26

arxiv.org/abs/math/0508541v1

Mathematics

Geometric Topology

14 pages. To appear in a book to be edited by Benson Farb containing open problems on mapping class groups

Scientific paper

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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