# Hebrew University Topology and Geometry Seminar

March 16, 2016

1100-1235

Ross building, Seminar Room 70A

## Sara Tukachinsky

*Hebrew University
*

##
Point-like bounding chains in open Gromov-Witten theory

**Abstract:**
Over a decade ago Welschinger defined invariants of real symplectic manifolds of complex dimensions 2 and 3, which count $J$-holomorphic disks with boundary and interior point constraints.
Since then, the problem of extending the definition to higher dimensions has attracted much attention.

We generalize Welschinger's invariants with boundary and interior constraints to higher odd dimensions using the language of $A_\infty$-algebras and bounding chains.
The bounding chains play the role of boundary point constraints. The geometric structure of our invariants is expressed algebraically in a version of the open WDVV equations.
These equations give rise to recursive formulae which allow the computation of all invariants for $\mathbb{C}P^n$.

This is joint work with Jake Solomon.