Trisections and Ozsvath-Szabo cobordism invariants

TL;DR

This paper introduces a method to compute cobordism maps on Heegaard Floer homology using trisection maps of smooth, compact four-manifolds, linking geometric decompositions to algebraic invariants.

Contribution

It provides a novel approach to calculating Ozsvath-Szabo cobordism invariants via trisection data, bridging geometric and algebraic topology.

Findings

Demonstrates how to derive cobordism maps from trisection maps

Establishes a new computational framework for Heegaard Floer invariants

Connects trisection theory with Ozsvath-Szabo invariants

Abstract

Given a smooth, compact four-manifold $X$ viewed as a cobordism from the empty set to its connected boundary, we demonstrate how to use the data of a trisection map $\pi:X^{4} \to \mathbb{D}^{2}$ to compute the induced cobordism maps on Heegaard Floer homology associated to $X$.