Topology Seminar by Peter Patzt

Algebra/Topology Seminar

Speaker: Peter Patzt (FU Berlin)

Title: The second homology of the Torelli groups (j/w Jeremy Miller and Jennifer C. Wilson)

Abstract: The homology of the pure braid group on n strands is a representation of the symmetric group on n letters. This prevents the pure braid groups from satisfying homological stability. Church and Farb describe the behavior of the homology with growing number of strands via the broader notion of representation stability. Later Putman and Sam describe it via central stability. Similarly the homology of the Torelli subgroup of the mapping class group of a connected oriented surface with genus g and one boundary component is a representation of Sp_g Z. Except for the first homology, little is know about the homology of the Torelli groups. We prove that the second homology is centrally stable.