### Rational cobordisms and integral homology (JungHwan Park)

- Series
- Geometry Topology Seminar
- Time
- Monday, September 10, 2018 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Rational cobordisms and integral homology – School of Mathematics Georgia Institute of Technology – junghwan.park@math.gatech.edu

We show that for any connected sum of lens spaces L there exists a connected sum of lens spaces X such that X is rational homology cobordant to L and if Y is rational homology cobordant to X, then there is an injection from H_1(X; Z) to H_1(Y; Z). Moreover, as a connected sum of lens spaces, X is uniquely determined up to orientation preserving diffeomorphism. As an application, we show that the natural map from the Z/pZ homology cobordism group to the rational homology cobordism group has large cokernel, for each prime p. This is joint work with Paolo Aceto and Daniele Celoria.