Low Dimensional Geometry and Topology Special Feature: Tour of bordered Floer theory
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A tour of bordered Floer theory
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 4dimensional 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 struc...
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We construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented two-manifold a di erential graded algebra. For a three-manifold with speci ed boundary, the invariant comes in two di erent versions, one of which (type D) is a module over the algebra and the other of which (type A) is an A∞ module. Both are well-de ned up to chain homotopy equivale...
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