• Corpus ID: 56012431

Bordered Floer homology for manifolds with torus boundary via immersed curves

@article{Hanselman2016BorderedFH,
  title={Bordered Floer homology for manifolds with torus boundary via immersed curves},
  author={Jonathan Hanselman and Jacob Rasmussen and Liam Watson},
  journal={arXiv: Geometric Topology},
  year={2016}
}
This paper gives a geometric interpretation of bordered Heegaard Floer homology for manifolds with torus boundary. If $M$ is such a manifold, we show that the type D structure $\widehat{\mathit{CFD}}$ may be viewed as a set of immersed curves decorated with local systems in $\partial M$. These curves-with-decoration are invariants of the underlying three-manifold up to regular homotopy of the curves and isomorphism of the local systems. Given two such manifolds and a homeomorphism $h$ between… 
Immersed curves in Khovanov homology
We give a geometric interpretation of Bar-Natan's universal invariant for the class of tangles in the 3-ball with four ends: we associate with such 4-ended tangles $T$ multicurves
Heegaard Floer homology for manifolds with torus boundary: properties and examples
This is a companion paper to earlier work of the authors, which interprets the Heegaard Floer homology for a manifold with torus boundary in terms of immersed curves in a punctured torus. We prove a
Bordered invariants of pairs of sutured manifolds with torus boundary
We establish a framework for extending invariants of sutured manifolds to invariants of pairs of sutured manifolds who differ by attaching a basic slice along a torus boundary component. In the
Order-detection of slopes on the boundaries of knot manifolds
. Motivated by the L -space conjecture, we investigate various notions of order-detection of slopes on knot manifolds. These notions are designed to characterise when rational homology 3-spheres
Instanton Floer homology, sutures, and Heegaard diagrams
This paper establishes a new technique that enables us to access some fundamental structural properties of instanton Floer homology. As an application, we establish, for the first time, a relation
Fukaya categories of surfaces, spherical objects and mapping class groups
Abstract We prove that every spherical object in the derived Fukaya category of a closed surface of genus at least $2$ whose Chern character represents a nonzero Hochschild homology class is
Integral Klein bottle surgeries and Heegaard Floer homology
We study gluings $X$ of the twisted $I$-bundle over the Klein bottle to knot complements, and investigate which gluings can be realizable as integral Dehn surgery along a knot in $S^3$. Closed,
Taut foliations in branched cyclic covers and left-orderable groups
  • S. Boyer, Ying Hu
  • Mathematics
    Transactions of the American Mathematical Society
  • 2019
We study the left-orderability of the fundamental groups of cyclic branched covers of links which admit co-oriented taut foliations. In particular we do this for cyclic branched covers of fibred
Thin links and Conway spheres
When restricted to alternating links, both Heegaard Floer and Khovanov homology concentrate along a single diagonal δ-grading. This leads to the broader class of thin links that one would like to
Almost $\iota$-complexes as immersed curves
Here the existence of a new homomorphism $P_{\omega} : \Theta_{\mathbb{Z}}^3 \to \mathbb{Z}$ is proven and the existence of a $\mathbb{Z}^{\infty}$ summand in $\Theta_{\mathbb{Z}}^3$ is reproven.
...
...

References

SHOWING 1-10 OF 42 REFERENCES
A calculus for bordered Floer homology
We consider a class of manifolds with torus boundary admitting bordered Heegaard Floer homology of a particularly simple form, namely, the type D structure may be described graphically by a disjoint
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 with
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 this
Foliations, orders, representations, L-spaces and graph manifolds
The decategorification of bordered Heegaard Floer homology
Bordered Heegaard Floer homology is an invariant for 3-manifolds, which associates to a surface F an algebra A(Z), and to a 3-manifold Y with boundary, together with an orientation-preserving
Bordered Floer homology and existence of incompressible tori in homology spheres
Let $Y$ be a homology sphere which contains an incompressible torus. We show that $Y$ cannot be an $L$ -space, i.e. the rank of $\widehat{\text{HF}}(Y)$ is greater than $1$ . In fact, if the homology
On L-spaces and left-orderable fundamental groups
Examples suggest that there is a correspondence between L-spaces and three-manifolds whose fundamental groups cannot be left-ordered. In this paper we establish the equivalence of these conditions
AN INTRODUCTION TO KNOT FLOER HOMOLOGY
This is a survey article about knot Floer homology. We present three constructions of this invariant: the original one using holomorphic disks, a combinatorial description using grid dia- grams, and
Fukaya categories of the torus and Dehn surgery
TLDR
It is shown that A∞-structures on the graded algebra A formed by the cohomology of two basic objects in the Fukaya category of the punctured 2-torus are governed by just two parameters (m6, m8), extracted from the Hochschild cohmology of A.
Floer simple manifolds and L-space intervals
...
...