Bordism Invariants of the Mapping Class Group

Aaron Heap

KNOTS in WASHINGTON XV (2nd Japan-USA Workshop in Knot Theory)
January 10-15, 2003
George Washington University and Johns Hopkins University
Washington, DC and Baltimore, MD, USA

Organizers
Kazuaki Kobayashi, Jozef H. Przytycki, Yongwu Rong, Shin-ichi Suzuki, Kouki Taniyama, Tatsuya Tsukamoto, Akira Yasuhara

Conference Homepage

Bordism Invariants of the Mapping Class Group
by
Aaron Heap
Rice University

We consider a 3-manifold M with an embedded, two-sided surface S in M. Let G denote the fundamental group of M and G_k denote the lower central series of G. Let g be a continuous map from M to the Eilenberg-MacLane space K(G/G_k, 1). Consider modifying M by removing a regular neighborhood of S and reattaching it via some surface homeomorphism f from the mapping class group, thus obtaining a new 3-manifold M(f). We also get a continuous map g(f) from M(f) to K(G/G_k, 1) by altering g. Let J(n) denote the generalized Johnson subgoup of the mapping class group of S. We show that if f is in J(2k-1) then (M(f), g(f)) and (M, g) are bordant over K(G/G_k, 1).

Date received: October 24, 2002