A tour of bordered Floer theory
Robert Lipshitz, Peter S. Ozsvath, and Dylan P. Thurston
TL;DR
This paper surveys bordered Floer theory, an extension of Heegaard Floer homology that applies to 3-manifolds with boundary, highlighting its formal structure and computational applications.
Contribution
It provides a comprehensive overview of the formal structure, construction, and computational aspects of bordered Floer homology, expanding the understanding of Heegaard Floer theory.
Findings
Explains the formal structure of bordered Floer homology.
Shows how to compute aspects of Heegaard Floer theory using bordered Floer methods.
Highlights the gluing properties and applications to 3-manifolds with boundary.
Abstract
Heegaard Floer theory is a kind of topological quantum field theory, assigning graded groups to closed, connected, oriented 3-manifolds and group homomorphisms to smooth, oriented 4-dimensional cobordisms. Bordered Heegaard Floer homology is an extension of Heegaard Floer homology to 3-manifolds with boundary, with extended-TQFT-type gluing properties. In this survey, we explain the formal structure and construction of bordered Floer homology and sketch how it can be used to compute some aspects of Heegaard Floer theory.
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