Covering spaces and Q-gradings on Heegaard Floer homology

Lee, Dan A.; Lipshitz, Robert

doi:10.4310/jsg.2008.v6.n1.a3

Cited by 14 publications

(15 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One easily constructs such a Heegaard diagram which, in fact, is a grid diagram for K in S 3 in the traditional sense [MOS06]. A simple formula for the Maslov grading [MOST06] in the cover, coupled with the relative Maslov index formula of [LL06] and a calculation of the absolute Maslov grading for a single generator completes the proof.…”

Section: 32mentioning

confidence: 85%

Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology

Baker

Grigsby

Hedden

2008

International Mathematics Research Notices

149

View full text Add to dashboard Cite

Abstract. Similar to knots in S 3 , any knot in a lens space has a grid diagram from which one can combinatorially compute all of its knot Floer homology invariants. We give an explicit description of the generators, differentials, and rational Maslov and Alexander gradings in terms of combinatorial data on the grid diagram. Motivated by existing results for the Floer homology of knots in S 3 and the similarity of the resulting combinatorics presented here, we conjecture that a certain family of knots is characterized by their Floer homology. Coupled with work of the third author, an affirmative answer to this would prove the Berge conjecture, which catalogs the knots in S 3 admitting lens space surgeries.

show abstract

Section: 32mentioning

confidence: 85%

Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology

Baker

Grigsby

Hedden

2008

International Mathematics Research Notices

149

View full text Add to dashboard Cite

show abstract

“…Let N κ be the double cover of S 3 branched along κ. If we consider the tori T ℘ , (β × id)(T ℘ ) as lying inside Sym m (X inv ), they are the Heegaard tori for a Morse function on N κ #S 1 × S 2 with two local minima and maxima, as in [12]. Moreover, these tori are weakly admissible, compare [14,Proposition 7.4].…”

Section: From Symplectic Khovanov To Heegaard Floermentioning

confidence: 99%

Localization for Involutions in Floer Cohomology

Seidel

Smith²

2010

Geom. Funct. Anal.

106

View full text Add to dashboard Cite

Abstract. We consider Lagrangian Floer cohomology for a pair of Lagrangian submanifolds in a symplectic manifold M . Suppose that M carries a symplectic involution, which preserves both submanifolds. Under various topological hypotheses, we prove a localization theorem for Floer cohomology, which implies a Smith-type inequality for the Floer cohomology groups in M and its fixed point set. Two applications to symplectic Khovanov cohomology are included.

show abstract

“…from the Heegaard triple diagram had the same evaluation on the generator H(Q) of H 2 (W ) (with the opposite sign because of the opposite orientation of the cobordism), see Equation (4). Since also F 2 = H(Q) 2 , it follows that the Spin c structures coincide on W : s z (u) = t i,j | W .…”

Section: Classes With Two Generatorsmentioning

confidence: 99%

Double plumbings of disk bundles over spheres

Horvat

2015

Communications in Analysis and Geometry

View full text Add to dashboard Cite

We consider double plumbings of two disk bundles over spheres. We calculate the Heegaard-Floer homology with its absolute grading of the boundary of such a plumbing. Given a closed smooth 4-manifold X and a suitable pair of classes in H 2 (X), we investigate when this pair of classes may be represented by a configuration of surfaces in X whose regular neighborhood is a double plumbing of disk bundles over spheres. Using similar methods we study single plumbings of two disk bundles over spheres inside X.

show abstract

Covering spaces and Q-gradings on Heegaard Floer homology

Abstract: . In this paper, we describe an alternate construction of this relative Q-grading by studying the Heegaard Floer homology of covering spaces.

Cited by 14 publications

References 11 publications

Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology

Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology

Localization for Involutions in Floer Cohomology

Double plumbings of disk bundles over spheres

Contact Info

Product

Resources

About