A tour of bordered Floer theory

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.

13 pages, 7 figures

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Cited by in corpus (10)

• Concordance homomorphisms from knot Floer homology
• A tour of bordered Floer theory
• Floer homology, group orderability, and taut foliations of hyperbolic 3-manifolds
• The combinatorics of Morse theory with boundary
• DG structures on odd categorified quantum sl(2)
• $SO(3)$-Floer homology of 3-manifolds with boundary 1
• Presentations for Generalized nilHecke Algebras
• Heegaard Floer Homologies: lecture notes
• Bordered Floer Homology of (2,2n)-Torus Link Complement
• Embedded Morse theory and relative splitting of cobordisms of manifolds