Connected Floer homology of covering involutions

Alfieri, Antonio; Kang, Singon; Stipsicz, András I.

doi:10.48550/arxiv.1905.11613

Cited by 2 publications

(8 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Though these examples do not bound corks, exploiting the equivariant 2-handle cobordisms constructed in Section 5 will allow us to use these computations to produce the families of strong corks claimed in Section 1. One input here comes from the work of Alfieri-Kang-Stipsicz [AKS19], who showed that if τ is the involution on Y " Σpp, q, rq obtained by viewing Y as the double branched cover of the Montesinos knot kpp, q, rq, then τ » ι. In fact, thanks to the following theorem (implicit in [BO91] and [MS13]), all we will need from their work is that there exists a geometric involution on Y which acts as ι on CF ´pY q: Theorem 7.6.…”

Section: Results and Computationsmentioning

confidence: 99%

“…A secondary aim for our study is to provide invariants of Θ τ Z{2Z which capture this additional concordance information. (Related ideas were independently considered and developed in [AKS19].) The methods of this paper apply equally well to this modified group, and in fact all of our examples are strongly non-extendable over any Z{2Z-homology ball.…”

Section: Introductionmentioning

confidence: 86%

“…To constrain the invariants of this manifold, we leverage some simple calculations coming from involutive Heegaard Floer homology. We have included this computation to demonstrate that in favorable situations, one can apply our techniques to other "base cases" than the manifolds established in [AKS19], so as to create more examples of strong corks.…”

Section: • • •mentioning

confidence: 99%

“…This notion was introduced by Hendricks, Manolescu, and Zemke [HMZ18], who defined ι-complexes in their work on involutive Heegaard Floer homology. The reader should also consult the work of Alfieri, Kang, and Stipsicz [AKS19], who carry out a similar strategy in the setting where Y is the double branched cover of a knot. The primary tool for our study comes from the following theorem:…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Corks, involutions, and Heegaard Floer homology

Dai¹,

Hedden²,

Mallick³

2020

Preprint

View full text Add to dashboard Cite

Building on the algebraic framework developed by Hendricks, Manolescu, and Zemke, we introduce and study a set of Floer-theoretic invariants aimed at detecting corks. Our invariants obstruct the extension of a given involution over any homology ball, rather than a particular contractible manifold. Unlike previous approaches, we do not utilize any closed 4-manifold topology or contact topology. Instead, we adapt the formalism of local equivalence coming from involutive Heegaard Floer homology. As an application, we define a modification Θ τ Z of the homology cobordism group which takes into account an involution on each homology sphere, and prove that this admits a Z 8 -subgroup of strongly non-extendable corks. The group Θ τ Z can also be viewed as a refinement of the bordism group of diffeomorphisms. Using our invariants, we furthermore establish several new families of corks and prove that various known examples are strongly non-extendable. Our main computational tool is a monotonicity theorem which constrains the behavior of our invariants under equivariant negative-definite cobordisms, and an explicit method of constructing such cobordisms via equivariant surgery.

show abstract

Section: Results and Computationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 86%

Section: • • •mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Corks, involutions, and Heegaard Floer homology

Dai¹,

Hedden²,

Mallick³

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…As shown in [AKS19], the behaviors of two involutions τ and ι of HF (Σ(K)) are a bit different: sometimes they are identical, whereas sometimes they are not. To be precise, we know the following:…”

Section: Involutions On Hfmentioning

confidence: 99%

Link homology theories and ribbon concordances

Kang¹

2019

Preprint

Self Cite

View full text Add to dashboard Cite

It was recently proved by several authors that ribbon concordances induce injective maps in knot Floer homology, Khovanov homology, and the Heegaard Floer homology of the branched double cover. We give a simple proof of a similar statement in a more general setting, which includes knot Floer homology, Khovanov-Rozansky homologies, and all conic strong Khovanov-Floer theories. This gives a philosophical answer to the question of which aspects of a link TQFT make it injective under ribbon concordances.2010 Mathematics Subject Classification. 57M27.

show abstract

Connected Floer homology of covering involutions

Cited by 2 publications

References 0 publications

Corks, involutions, and Heegaard Floer homology

Corks, involutions, and Heegaard Floer homology

Link homology theories and ribbon concordances

Contact Info

Product

Resources

About