scholarly journals A link surgery spectral sequence in monopole Floer homology

2011 ◽  
Vol 226 (4) ◽  
pp. 3216-3281 ◽  
Author(s):  
Jonathan M. Bloom
Keyword(s):  
Spectral Sequence ◽  
Floer Homology ◽  
Link Surgery

scholarly journals Bordered Floer homology and the spectral sequence of a branched double cover II: the spectral sequences agree

2016 ◽  
Vol 9 (2) ◽  
pp. 607-686
Author(s):  
Robert Lipshitz ◽  
Peter S. Ozsváth ◽  
Dylan P. Thurston
Keyword(s):  
Spectral Sequence ◽  
Floer Homology ◽  
Double Cover ◽  
Spectral Sequences

scholarly journals Khovanov homology and knot Floer homology for pointed links

2017 ◽  
Vol 26 (02) ◽  
pp. 1740004 ◽  
Author(s):  
John A. Baldwin ◽  
Adam Simon Levine ◽  
Sucharit Sarkar
Keyword(s):  
Spectral Sequence ◽  
Floer Homology ◽  
Khovanov Homology ◽  
Knot Floer Homology ◽  
Text Page ◽  
Text Component

A well-known conjecture states that for any [Formula: see text]-component link [Formula: see text] in [Formula: see text], the rank of the knot Floer homology of [Formula: see text] (over any field) is less than or equal to [Formula: see text] times the rank of the reduced Khovanov homology of [Formula: see text]. In this paper, we describe a framework that might be used to prove this conjecture. We construct a modified version of Khovanov homology for links with multiple basepoints and show that it mimics the behavior of knot Floer homology. We also introduce a new spectral sequence converging to knot Floer homology whose [Formula: see text] page is conjecturally isomorphic to our new version of Khovanov homology; this would prove that the conjecture stated above holds over the field [Formula: see text].

scholarly journals Cap-product structures on the Fintushel–Stern spectral sequence

2001 ◽  
Vol 131 (2) ◽  
pp. 265-278
Author(s):  
WEIPING LI
Keyword(s):  
Spectral Sequence ◽  
Floer Homology ◽  
Homology Class ◽  
Product Structure ◽  
Point Of View ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Product Structures

We show that there is a well-defined cap-product structure on the Fintushel–Stern spectral sequence and the induced cap-product structure on the ℤ8-graded instanton Floer homology. The cap-product structure provides an essentially new property of the instanton Floer homology, from a topological point of view, which multiplies a finite-dimensional cohomlogy class by an infinite-dimensional homology class (Floer cycles) to get another infinite-dimensional homology class.

scholarly journals Bordered Floer homology and the spectral sequence of a branched double cover I

2014 ◽  
Vol 7 (4) ◽  
pp. 1155-1199 ◽  
Author(s):  
Robert Lipshitz ◽  
Peter S. Ozsváth ◽  
Dylan P. Thurston
Keyword(s):  
Spectral Sequence ◽  
Floer Homology ◽  
Double Cover

scholarly journals Curved Rickard complexes and link homologies

2020 ◽  
Vol 2020 (769) ◽  
pp. 87-119
Author(s):  
Sabin Cautis ◽  
Aaron D. Lauda ◽  
Joshua Sussan
Keyword(s):  
Spectral Sequence ◽  
Quantum Groups ◽  
Braid Group ◽  
Derived Categories ◽  
Duke Math ◽  
Khovanov Homology ◽  
Hilbert Schemes ◽  
Coherent Sheaves ◽  
Knot Homology ◽  
Original Motivation

AbstractRickard complexes in the context of categorified quantum groups can be used to construct braid group actions. We define and study certain natural deformations of these complexes which we call curved Rickard complexes. One application is to obtain deformations of link homologies which generalize those of Batson–Seed [3] [J. Batson and C. Seed, A link-splitting spectral sequence in Khovanov homology, Duke Math. J. 164 2015, 5, 801–841] and Gorsky–Hogancamp [E. Gorsky and M. Hogancamp, Hilbert schemes and y-ification of Khovanov–Rozansky homology, preprint 2017] to arbitrary representations/partitions. Another is to relate the deformed homology defined algebro-geometrically in [S. Cautis and J. Kamnitzer, Knot homology via derived categories of coherent sheaves IV, colored links, Quantum Topol. 8 2017, 2, 381–411] to categorified quantum groups (this was the original motivation for this paper).

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