English

Towards representation stability for the second homology of the Torelli group

Algebraic Topology 2011-02-03 v2 Representation Theory

Abstract

We show for g > 6 that the second homology group of the Torelli group of a surface of genus g and 1 boundary component is generated as an Sp(2g,Z)-module by the image under the stabilization map of the second homology group of the Torelli group of a surface of genus 6 and 1 boundary component. In the process we also show that the quotient of the complex of arcs with identity permutation by the Torelli group is (g-2)-connected, for one or two boundary components.

Keywords

Cite

@article{arxiv.1101.5767,
  title  = {Towards representation stability for the second homology of the Torelli group},
  author = {Søren K. Boldsen and Mia Hauge Dollerup},
  journal= {arXiv preprint arXiv:1101.5767},
  year   = {2011}
}

Comments

36 pages