Home

Robert Lipshitz

  1. Bordered Floer homology and the branched double cover I.

    Wed, 11/03/2010 - 16:01 — SomNambul
    Authors: Robert Lipshitz, Dylan P. Thurston, Peter S. Ozsváth
    Subjects: Geometric Topology
    Abstract

    Given a link in the three-sphere, Z. Szab\'o and the second author
    constructed a spectral sequence starting at the Khovanov homology of the link
    and converging to the Heegaard Floer homology of its branched double-cover. The
    aim of this paper and its sequel is to explicitly calculate this spectral
    sequence, using bordered Floer homology. There are two primary ingredients in
    this computation: an explicit calculation of filtered bimodules associated to
    Dehn twists and a pairing theorem for polygons.

  2. Heegaard Floer homology as morphism spaces.

    Mon, 05/10/2010 - 15:01 — SomNambul
    Authors: Robert Lipshitz, Dylan P. Thurston, Peter S. Ozsváth
    Subjects: Geometric Topology
    Abstract

    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 formulation is closer in spirit
    to the usual TQFT framework, and allows a more direct comparison with
    Fukaya-categorical constructions. The result also leads to various dualities in
    bordered Floer homology.

  3. Bimodules in bordered Heegaard Floer homology.

    Wed, 03/03/2010 - 16:01 — SomNambul
    Authors: Robert Lipshitz, Dylan P. Thurston, Peter S. Ozsvath
    Subjects: Geometric Topology
    Abstract

    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 paper, we establish
    naturality properties of this invariant. Changing the diffeomorphism between F
    and the boundary of Y tensors the bordered invariant with a suitable bimodule
    over A(F). These bimodules give an action of a suitably based mapping class
    group on the category of modules over A(F).

  4. Bordered Heegaard Floer homology: Invariance and pairing.

    Wed, 11/18/2009 - 16:01 — SomNambul
    Authors: Peter Ozsvath, Dylan Thurston, Robert Lipshitz
    Subjects: Geometric Topology
    Abstract

    We construct Heegaard Floer theory for 3-manifolds with connected boundary.
    The theory associates to an oriented two-manifold a differential graded
    algebra. For a three-manifold with specified boundary, the invariant comes in
    two different versions, one of which (type D) is a module over the algebra and
    the other of which (type A) is an A-infinity module. Both are well-defined up
    to chain homotopy equivalence.

Math-arch

Syndicate content