Moving basepoints and the induced automorphisms of link Floer homology

By Sucharit Sarkar. 2011

63 citations recorded by the source corpus.

Given an l-component pointed oriented link (L,p) in an oriented three-manifold Y, one can construct its link Floer chain complex CFL(Y,L,p) over the polynomial ring F_2[U_1,...,U_l]. Moving the basepoint p_i in the link component L_i once around induces an automorphism of CFL(Y,L,p). In this paper, we study an automorphism (a possibly different one) of CFL(Y,L,p) defined explicitly in terms of holomorphic disks; for links in S^3, we show that these two automorphisms are the same.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5a7cdc4d05454831aeba38b486b51c27f3916902

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Citations in the corpus

Link cobordisms and functoriality in link Floer homology (2016, methodology): “e surface, along an edge. The eect to the link cobordism maps is to insert the dieomorphism map corresponding to a twist around a link component, at various stages. We can use Sarkar’s formula from [Sar11a] (proven in [Zem16] for the versions of link Floer homology we are working with) to see that t”
Naturality and Mapping Class Groups in Heegaard Floer Homology (2012, background): “In this context, Sarkar [21] has constructed examples where the action of π1(S 1) on ĤFK (K, p) is non-trivial.”
Knot Floer homology obstructs ribbon concordance (2019, methodology): “K 0 or K 1 in one full twist. Note that composition with a grading preserving automorphism does not aect the statement of Theorem1.1. The basepoint moving automorphism map has been studied by Sarkar [Sar15] and by the author [Zem17]. Next, we discuss gradings. If L is a null-homologous link in Y (i.”
Connected sums and involutive knot Floer homology (2017, background): “The maps Φi and Ψi appear frequently in the link Floer TQFT [11, 38], however they appeared earlier in work of Sarkar on diffeomorphism maps on knot Floer homology [33].”
Involutive Heegaard Floer homology (2015, methodology): “The key observation is that ι(2)K is equal to the map studied by Sarkar in [52], which corresponds to moving the basepoints around the knot.”
On the geography and botany of knot Floer homology (2014, background): “ H∗(HFK\(K),∂K) ∼= ( F if m = 0 0 otherwise. 1At present, the theory lacks the functoriality with respect to cobordisms desired by a true categoriﬁcation, but this structure is expected to exist. See [22, 84, 85] for partial results in this direction. ON THE GEOGRAPHY AND BOTANY OF KNOT FLOER HOMOLO”