Homological infiniteness of decorated Torelli groups and Torelli spaces (Q5937399)

The author improves on his earlier result [Topology 40, No. 2, 213-221 (2001; Zbl 0979.57005)]: for genus \(g\geq 7\) and any number \(n\) of marked points and \(r\) of embedded disks the rational homology of the Torelli group \({\mathcal T}^n_{g,r}\) is infinite dimensional. Using a spectral sequence argument he proves that if the homology of \({\mathcal T}^n_g\) is infinite dimensional then so is that of \({\mathcal T}^{n+1}_g\). This gives the necessary induction step to deduce the result from previous work.NEWLINENEWLINENEWLINEThe Torelli group acts freely on the associated Teichmüller space. The quotient, so-called Torelli space, is a finite dimensional complex manifold and a model for the classifying space. Thus its homology is also infinite dimensional.NEWLINENEWLINENEWLINEReviewer's remark: In particular the homology vanishes in dimensions \(> 6g- 6 + 2n + 4r\).