30 citations · 109 across the 13 of their papers we have counts for
16 papers
Real bordered Floer homology
Robert Lipshitz, Peter Ozsváth
Fix a 3-manifold with boundary and an orientation-preserving involution exchanging the boundary components, with nonempty fixed set. To an appropriate k…
Floer homology beyond borders
Robert Lipshitz, Peter Ozsváth, Dylan Thurston
Bordered Floer homology is an invariant for 3-manifolds with boundary, defined by the authors in 2008. It extends the Heegaard Floer homology of closed 3-manifolds, defined in earl…
Bordered HF- for three-manifolds with torus boundary
Robert Lipshitz, Peter Ozsváth, Dylan Thurston
We define an invariant for bordered 3-manifolds with torus boundary, taking the form of a module over a weighted A-infinity algebra associated to a torus defined in previous work.…
A bordered HF- algebra for the torus
Robert Lipshitz, Peter Ozsváth, Dylan Thurston
We describe a weighted -algebra associated to the torus. We give a combinatorial construction of this algebra, and an abstract characterization. The abstract characteriza…
Diagonals and A-infinity Tensor Products
Robert Lipshitz, Peter Ozsváth, Dylan Thurston
Extending work of Saneblidze-Umble and others, we use diagonals for the associahedron and multiplihedron to define tensor products of A-infinity algebras, modules, algebra homomorp…
Combinatorial Heegaard Floer homology and sign assignments
Peter Ozsváth, András I. Stipsicz, Zoltán Szabó
We provide an intergral lift of the combinatorial definition of Heegaard Floer homology for nice diagrams, and show that the proof of independence using convenient diagrams adapts…
Relative Q-gradings from bordered Floer theory
Robert Lipshitz, Peter Ozsváth, Dylan Thurston
In this paper we show how to recover the relative Q-grading in Heegaard Floer homology from the noncommutative grading on bordered Floer homology.
Notes on bordered Floer homology
Robert Lipshitz, Peter Ozsváth, Dylan Thurston
This is a survey of bordered Heegaard Floer homology, an extension of the Heegaard Floer invariant HF-hat to 3-manifolds with boundary. Emphasis is placed on how bordered Heegaard…
Knots in lattice homology
Peter Ozsváth, András Stipsicz, Zoltán Szabó
Assume that Γ_{v_0} is a tree with vertex set Vert(Γ_{v_0})={v_0, v_1,..., v_n}, and with an integral framing (weight) attached to each vertex except v_0. Assume furthermore that t…
Knot lattice homology in L-spaces
Peter Ozsváth, András Stipsicz, Zoltán Szabó
We show that the knot lattice homology of a knot in an L-space is equivalent to the knot Floer homology of the same knot (viewed these invariants as filtered chain complexes over t…
A spectral sequence on lattice homology
Peter Ozsváth, András I. Stipsicz, Zoltán Szabó
Using the link surgery formula for Heegaard Floer homology we find a spectral sequence from the lattice homology of a plumbing tree to the Heegaard Floer homology of the correspond…
A faithful linear-categorical action of the mapping class group of a surface with boundary
Robert Lipshitz, Peter S. Ozsváth, Dylan P. Thurston
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 introducti…
Computing HF^ by factoring mapping classes
Robert Lipshitz, Peter S. Ozsváth, Dylan P. Thurston
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…
Heegaard Floer homology as morphism spaces
Robert Lipshitz, Peter S. Ozsváth, Dylan P. Thurston
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.…
Heegaard Floer invariants of Legendrian knots in contact three--manifolds
Paolo Lisca, Peter Ozsváth, András I. Stipsicz +1
We define invariants of null--homologous Legendrian and transverse knots in contact 3--manifolds. The invariants are determined by elements of the knot Floer homology of the underl…
Seiberg--Witten Monopoles on Seifert Fibered Spaces
Tomasz S. Mrowka, Peter S. Ozsváth, Baozhen Yu
In this paper, we investigate the Seiberg-Witten gauge theory for Seifert fibered spaces. The monopoles over these three-manifolds, for a particular choice of metric and perturbati…