L‐space surgeries on 2‐component L‐space links

Liu, Beibei

doi:10.1112/tlm3.12027

Cited by 3 publications

(1 citation statement)

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“…Then we will use the fact that knot Floer homology detects genus to show that J n is detected among 2-component links with unknotted components. The topological argument used here was communicated to the authors by Eugene Gorsky (2020), and also appears in Liu's classification of the links T .2; 2n/ in terms of surgery to a Heegaard Floer L-space [25].…”

Section: Knot Floer Homology Detects J Nmentioning

confidence: 96%

Knot Floer homology, link Floer homology and link detection

Binns,

Martin

2024

Algebr. Geom. Topol.

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We give new link detection results for knot and link Floer homology, inspired by recent work on Khovanov homology. We show that knot Floer homology detects T .2; 4/, T .2; 6/, T .3; 3/, L7n1 and the link T .2; 2n/ with the orientation of one component reversed. We show link Floer homology detects T .2; 2n/ and T .n; n/, for all n. Additionally, we identify infinitely many pairs of links such that both links in the pair are each detected by link Floer homology but have the same Khovanov homology and knot Floer homology. Finally, we use some of our knot Floer detection results to give topological applications of annular Khovanov homology. Knot Floer homology and link Floer homologyKnot Floer homology and link Floer homology are invariants of links in S 3 , defined using a version of Lagrangian Floer homology [31; 32; 34]. They are categorifications of the single variable and multivariable Alexander polynomials, respectively. Here we briefly highlight the key features of knot Floer homology and link Floer homology that we use to obtain our detection results. We work with coefficients in Z=2Z.

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Section: Knot Floer Homology Detects J Nmentioning

confidence: 96%

Knot Floer homology, link Floer homology and link detection

Binns,

Martin

2024

Algebr. Geom. Topol.

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Fibered and strongly quasi-positive $L$-space links

Cavallo

Liu²

2020

Preprint

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Four manifolds with no smooth spines

Belegradek¹,

Liu²

2021

Preprint

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Let W be a compact smooth 4 -manifold that deformation retract to a pl embedded closed surface. One can arrange the embedding to have at most one non-locally-flat point, and near the point the topology of the embedding is encoded in the singularity knot K . If K is slice, then W has a smooth spine, i.e., deformation retracts onto a smoothly embedded surface. Using the obstructions from the Heegaard Floer homology and the high-dimensional surgery theory, we show that W has no smooth spines if K is a knot with nonzero Arf invariant, a nontrivial L-space knot, the connected sum of nontrivial L-space knots, or an alternating knot of signature < −4 . We also discuss examples where the interior of W is negatively curved.

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L‐space surgeries on 2‐component L‐space links

Cited by 3 publications

References 20 publications

Knot Floer homology, link Floer homology and link detection

Knot Floer homology, link Floer homology and link detection

Fibered and strongly quasi-positive $L$-space links

Four manifolds with no smooth spines

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