Contact Structures with Distinct Heegaard Floer Invariants

TL;DR

This paper demonstrates that different Stein structures on a 4-manifold induce contact structures on its boundary with unique Heegaard Floer invariants, highlighting a link between Stein structures and Floer theory.

Contribution

It establishes that non-homotopic Stein structures produce contact structures with distinct Heegaard Floer invariants, a novel connection in 4-manifold topology.

Findings

Distinct Stein structures lead to contact structures with different invariants

Heegaard Floer invariants distinguish non-homotopic Stein structures

New insights into the relationship between Stein structures and Floer theory

Abstract

We prove that the contact structures on Y= dX induced by non-homotopic Stein structures on the 4-manifold X have distinct Heegaard Floer invariants.