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A Khovanov stable homotopy type

- R. Lipshitz, S. Sarkar
- Mathematics
- 16 December 2011

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) is… Expand

A cylindrical reformulation of Heegaard Floer homology

- R. Lipshitz
- Mathematics
- 18 February 2005

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 entire… Expand

Bordered Heegaard Floer homology

- R. Lipshitz, P. Ozsvath, D. Thurston
- Mathematics
- Memoirs of the American Mathematical…
- 3 October 2008

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 with… Expand

Bimodules in bordered Heegaard Floer homology

- R. Lipshitz, P. Ozsvath, D. Thurston
- Mathematics
- 2 March 2010

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 this… Expand

A Steenrod square on Khovanov homology

- R. Lipshitz, S. Sarkar
- Mathematics
- 25 April 2012

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 interesting… Expand

Heegaard Floer homology as morphism spaces

- R. Lipshitz, Peter S. Ozsv'ath, D. Thurston
- Mathematics
- 7 May 2010

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 present… Expand

A Khovanov homotopy type

- R. Lipshitz, S. Sarkar
- Mathematics
- 16 December 2011

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) is… Expand

A faithful linear-categorical action of the mapping class group of a surface with boundary

- R. Lipshitz, Peter S. Ozsv'ath, D. Thurston
- Mathematics
- 5 December 2010

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

- R. Lipshitz, P. Ozsvath, D. Thurston
- Mathematics
- 3 October 2008

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 parametrized… Expand

Computing HF by factoring mapping classes

- R. Lipshitz, Peter S. Ozsv'ath, D. Thurston
- Mathematics
- 13 October 2010

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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