Surgery on links of linking number zero and the Heegaard Floer $d$-invariant

Gorsky, Eugene; Liu, Beibei; Moore, Allison H.

doi:10.4171/qt/137

Cited by 6 publications

(13 citation statements)

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“…In this section, we associate a finite rectangular CW‐complex to the truncated surgery complex for 2‐component L‐space links. We refer the reader to [4, Section 3.3] for more details. Each

A_{s}^{00}

in the truncated surgery complex corresponds to a 2‐cell.…”

Section: Surgery Complex and Truncationsmentioning

confidence: 99%

“…It is interesting to study the very negative L-space surgeries for type (B) L-space links. For example, Gorsky [4] are the same as the ones we define here when restricting to nontrivial 2-component links with unknotted components and vanishing linking number.…”

Section: Introductionmentioning

confidence: 99%

“…Theorem 1.5 [4,Theorem 5.1]. Assume that L is a nontrivial L-space link with unknotted components and linking number zero.…”

Section: Introductionmentioning

confidence: 99%

“…If the context is clear, we write

b_{i} false(scriptL false)

b_{i}

for simplicity. Note that the nonnegative integers

b_{1}, b_{2}

defined in [4] are the same as the ones we define here when restricting to nontrivial 2‐component links with unknotted components and vanishing linking number. Theorem Let

L = L_{1} \cup L_{2}

be a type (B) L‐space link with linking number

l

.…”

Section: Introductionmentioning

confidence: 99%

“…Then the generator of

H F^{-} false(S_{d_{1}, d_{2}}^{3} (L), frakturs false)

H_{*} false(A_{s}^{11} false)

for some

s \in H (L)

. For details, see Section 3.1 and [4]. This will give restrictions to the differentials in the surgery complex, which is related to the

H

‐function.…”

Section: Introductionmentioning

confidence: 99%

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

Liu

2021

Trans London Maths Soc

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In this paper, we analyze L-space surgeries on two component L-space links. We show that if one surgery coefficient is negative for the L-space surgery, then the corresponding link component is an unknot. If the link admits a very negative (that is, d1, d2 0) L-space surgery, it is either the unlink or the Hopf link. We also give a way to characterize the torus link T (2, 2l) by observing an L-space surgery S 3 d 1 ,d 2 (L) with some d1d2 < 0 on a 2-component L-space link with unknotted components. For some 2-component L-space links, we give explicit descriptions of the L-space surgery sets.

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A_{s}^{00}

in the truncated surgery complex corresponds to a 2‐cell.…”

Section: Surgery Complex and Truncationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Theorem 1.5 [4,Theorem 5.1]. Assume that L is a nontrivial L-space link with unknotted components and linking number zero.…”

Section: Introductionmentioning

confidence: 99%

“…If the context is clear, we write

b_{i} false(scriptL false)

b_{i}

for simplicity. Note that the nonnegative integers

b_{1}, b_{2}

defined in [4] are the same as the ones we define here when restricting to nontrivial 2‐component links with unknotted components and vanishing linking number. Theorem Let