I will first recall the definition of an invariant that assigns to any compact subset K of a closed symplectic manifold M a module SH_M(K) over the Novikov ring. I will go over the case of M=two sphere to illustrate various points about the invariant. Finally I will state the Mayer-Vietoris property and explain under what conditions it holds.

# Topology Seminar

For more information about this seminar, contact Zoltan Szabo, David Gabai, Francesco Lin, Peter Ozsvath, John Pardon or Jonathan Hanselman.

**Please click on seminar title for complete abstract.**

##### Mayer-Vietoris sequence for relative symplectic cohomology

MIT

##### The bipolar filtration of topologically slice knots

The bipolar filtration of Cochran, Harvey and Horn initiated the study of deeper structures of the smooth concordance group of the topologically slice knots. We show that the graded quotient of the bipolar filtration has infinite rank at each stage greater than one.

To detect nontrivial elements in the quotient, the proof uses higher order amenable Cheeger-Gromov $L^2$ $\rho$-invariants and infinitely many Heegaard Floer correction term $d$-invariants simultaneously.

This is joint work with Jae Choon Cha.

Korea Institute For Advanced Study

##### TBA - Cladius Zibrowius

Sherbrooke University

##### TBA - Raphael Zentner

University of Regensburg (Germany)

##### TBA - Aliakbar Daemi

SCGP

##### TBA - Tye Lidman

North Carolina State University