Tuesday Seminar on Topology

Seminar information archive ~04/13Next seminarFuture seminars 04/14~

Date, time & place Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.)
Organizer(s) KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya

2013/06/25

17:10-18:10   Room #056 (Graduate School of Math. Sci. Bldg.)
Tadayuki Watanabe (Shimane University)
Higher-order generalization of Fukaya's Morse homotopy
invariant of 3-manifolds (JAPANESE)
[ Abstract ]
In his article published in 1996, K. Fukaya constructed
a 3-manifold invariant by using Morse homotopy theory. Roughly, his
invariant is defined by considering several Morse functions on a
3-manifold and counting with weights the ways that the theta-graph can
be immersed such that edges follow gradient lines. We generalize his
construction to 3-valent graphs with arbitrary number of loops for
integral homology 3-spheres. I will also discuss extension of our method
to 3-manifolds with positive first Betti numbers.