A topological grading on bordered Heegaard Floer homology

```@article{Huang2012ATG,
title={A topological grading on bordered Heegaard Floer homology},
author={Yang Huang and Vinicius G. B. Ramos},
journal={arXiv: Geometric Topology},
year={2012}
}```
• Published 30 November 2012
• Mathematics
• arXiv: Geometric Topology
In this paper, we construct a canonical grading on bordered Heegaard Floer homology by homotopy classes of nonvanishing vector fields. This grading is a generalization of our construction of an absolute grading on Heegaard Floer homology and it extends the well-known grading with values in a noncommutative group defined by Lipshitz-Ozsv\'ath-Thurston.
The Alexander module, Seifert forms, and categorification
• Mathematics
• 2015
We show that bordered Floer homology provides a categorification of a topological quantum field theory (TQFT) described by Donaldson [Proceedings of the Kirbyfest, Berkeley, CA, 1998, Geometry &
An absolute Z/2 grading on bordered Heegaard Floer homology
Bordered Heegaard Floer homology is an invariant for 3-manifolds, which associates to a surface F an algebra A(F), and to a 3-manifold Y with boundary, together with an orientation-preserving
Heegaard Floer Homologies: lecture notes
These are lecture notes from a series of lectures at the SMF summer school on "Geometric and Quantum Topology in Dimension 3", June 2014. The focus is on Heegaard Floer homology from the perspective
On the Frøyshov invariant and monopole Lefschetz number
• Mathematics
• 2018
Given an involution on a rational homology 3-sphere \$Y\$ with quotient the \$3\$-sphere, we prove a formula for the Lefschetz number of the map induced by this involution in the reduced monopole Floer
NONSURJECTIVE SATELLITE OPERATORS AND PIECEWISE-LINEAR CONCORDANCE
We exhibit a knot \$P\$ in the solid torus, representing a generator of first homology, such that for any knot \$K\$ in the 3-sphere, the satellite knot with pattern \$P\$ and companion \$K\$ is not smoothly
On a Heegaard Floer theory for tangles
The purpose of this thesis is to define a "local" version of Ozsv\'{a}th and Szab\'{o}'s Heegaard Floer homology \$\operatorname{\widehat{HFL}}\$ for links in the 3-dimensional sphere, i.e. a Heegaard

References

SHOWING 1-7 OF 7 REFERENCES
An absolute grading on Heegaard Floer homology by homotopy classes of oriented 2-plane fields
• Mathematics
• 2011
For a closed oriented 3-manifold Y, we define an absolute grading on the Heegaard Floer homology groups of Y by homotopy classes of oriented 2-plane fields. We show that this absolute grading refines
Heegaard Floer homology as morphism spaces
• Mathematics
• 2011
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
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 entire
Classes d'homotopie de champs de vecteurs Morse-Smale sans singularit\'e sur les fibr\'es de Seifert
In the first part of this paper, we consider smooth maps from a compact orientable 3-manifold without boundary to the 2-sphere. We give a geometric criterion to decide whether two given maps are
Bordered Floer homology for sutured manifolds
We define a sutured cobordism category of surfaces with boundary and 3-manifolds with corners. In this category a sutured 3-manifold is regarded as a morphism from the empty surface to itself. In the
Holomorphic disks and three-manifold invariants: Properties and applications
• Mathematics
• 2001
In [27], we introduced Floer homology theories HF - (Y,s), HF∞(Y,s), HF + (Y, t), HF(Y,s),and HF red (Y, s) associated to closed, oriented three-manifolds Y equipped with a Spiny structures s ∈ Spin
Emmanuel Dufraine Classes d ’ homotopie de champs de vecteurs Morse - Smale sans singularité sur les fibrés de Seifert
• 2011