title: Tour of bordered Floer theory.
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.
authors.affiliation: Department of Mathematics, Columbia University, New York, NY 10027, USA.
authors.forename: Robert
authors.initials: R
authors.lastname: Lipshitz
authors.forename: Peter S
authors.initials: PS
authors.lastname: Ozsváth
authors.forename: Dylan P
authors.initials: DP
authors.lastname: Thurston