Geometry/topology Seminar

Mapping class groups of 4-manifolds with 1-handles

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Speaker(s): Boyu Zhang (The University of Maryland)
Budney-Gabai proved in 2019 that the mapping class group of S^1xD^3 relative to the boundary is an abelian group with infinite rank. In this talk, we will discuss a generalization of Budney-Gabai's result to 4-manifolds with 1-handles. We will show that if a manifold M is the boundary connected sum of a compact manifold N with S^1xD^3, such that either N has a trivial pi_2 or N is of the form IxY, then the mapping class group of M has a center with infinite rank. This talk is based on joint work with Jianfeng Lin and Yi Xie.

Physics 119