Notes on bordered Floer homology

TL;DR

This paper surveys bordered Heegaard Floer homology, an extension of HF-hat for 3-manifolds with boundary, focusing on its computational applications and methodology.

Contribution

It provides an overview of bordered Heegaard Floer homology and highlights its utility in computational topology.

Findings

Demonstrates how bordered Floer homology facilitates computations of 3-manifold invariants.

Summarizes key techniques and structures in bordered Heegaard Floer theory.

Shows potential for simplifying complex topological calculations.

Abstract

This is a survey of bordered Heegaard Floer homology, an extension of the Heegaard Floer invariant HF-hat to 3-manifolds with boundary. Emphasis is placed on how bordered Heegaard Floer homology can be used for computations.