Tour of bordered Floer theory

Robert Lipshitz, Peter S. Ozsváth, Dylan P. Thurston

Research output: Contribution to journalReview article

8 Scopus citations

Abstract

Heegaard Floer theory is a kind of topological quantum field theory (TQFT), assigning graded groups to closed, connected, oriented 3-manifolds and group homomorphisms to smooth, oriented four-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.

Original languageEnglish (US)
Pages (from-to)8085-8092
Number of pages8
JournalProceedings of the National Academy of Sciences of the United States of America
Volume108
Issue number20
DOIs
StatePublished - May 17 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General

Keywords

  • 4-manifolds
  • Heegaard Floer homology

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