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A Khovanov stable homotopy type
Given a link diagram L we construct spectra X j Kh(L) so that the Khovanov homology Kh(L) is isomorphic to the (reduced) singular cohomology H̃(X j Kh(L)). The construction of X j Kh(L) isExpand
A cylindrical reformulation of Heegaard Floer homology
We reformulate Heegaard Floer homology in terms of holomorphic curves in the cylindrical manifold U a0;1c R, where U is the Heegaard surface, instead of Sym g .U/. We then show that the entireExpand
Bordered Heegaard Floer homology
We construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold withExpand
Bimodules in bordered Heegaard Floer homology
Bordered Heegaard Floer homology is a three-manifold invariant which associates to a surface F an algebra A(F) and to a three-manifold Y with boundary identified with F a module over A(F). In thisExpand
A Steenrod square on Khovanov homology
In a previous paper, we defined a space-level version X(L) of Khovanov homology. This induces an action of the Steenrod algebra on Khovanov homology. In this paper, we describe the first interestingExpand
Heegaard Floer homology as morphism spaces
In this paper we prove another pairing theorem for bordered Floer homology. Unlike the original pairing theorem, this one is stated in terms of homomorphisms, not tensor products. The presentExpand
A Khovanov homotopy type
Given a link diagram L we construct spectra X^j(L) so that the Khovanov homology Kh^{i,j}(L) is isomorphic to the (reduced) singular cohomology H^i(X^j(L)). The construction of X^j(L) isExpand
A faithful linear-categorical action of the mapping class group of a surface with boundary
We show that the action of the mapping class group on bordered Floer homology in the second to extremal spin^c-structure is faithful. This paper is designed partly as an introduction to the subject,Expand
Slicing planar grid diagrams: a gentle introduction to bordered Heegaard Floer homology
We describe some of the algebra underlying the decomposition of planar grid diagrams. This provides a useful toy model for an extension of Heegaard Floer homology to 3-manifolds with parametrizedExpand
Computing HF by factoring mapping classes
Bordered Heegaard Floer homology is an invariant for three-manifolds with boundary. In particular, this invariant associates to a handle decomposition of a surface F a differential graded algebra,Expand
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