HF=HM I : Heegaard Floer homology and Seiberg--Witten Floer homology

TL;DR

This paper establishes an isomorphism between Heegaard Floer homology and Seiberg-Witten Floer homology for closed, oriented 3-manifolds, bridging two important invariants in low-dimensional topology.

Contribution

It constructs the first part of a series proving the isomorphism between Heegaard Floer and Seiberg-Witten Floer homologies.

Findings

First construction of the isomorphism for 3-manifolds

Provides foundational framework for subsequent parts

Bridges two major Floer homology theories

Abstract

Let M be a closed, connected and oriented 3-manifold. This article is the first of a five part series that constructs an isomorphism between the Heegaard Floer homology groups of M and the corresponding Seiberg-Witten Floer homology groups of M.