Knot Floer homology of satellite knots with (1, 1) patterns

Chen, Wenzhao

doi:10.1007/s00029-023-00859-6

Sel. Math. New Ser.

2023

DOI: 10.1007/s00029-023-00859-6

|View full text |Cite

Knot Floer homology of satellite knots with (1, 1) patterns

Wenzhao Chen

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Rank‐expanding satellites, Whitehead doubles, and Heegaard Floer homology

Dai,

Hedden,

Mallick

et al. 2024

Journal of Topology

View full text Add to dashboard Cite

We show that a large class of satellite operators are rank‐expanding; that is, they map some rank‐one subgroup of the concordance group onto an infinite linearly independent set. Our work constitutes the first systematic study of this property in the literature and partially affirms a conjecture of the second author and Pinzón‐Caicedo. More generally, we establish a Floer‐theoretic condition for a family of companion knots to have infinite‐rank image under satellites from this class. The methods we use are amenable to patterns that act trivially in topological concordance and are capable of handling a surprisingly wide variety of companions. For instance, we give an infinite linearly independent family of Whitehead doubles whose companion knots all have negative ‐invariant. Our results also recover and extend several theorems in this area established using instanton Floer homology.

show abstract

Rank‐expanding satellites, Whitehead doubles, and Heegaard Floer homology

Dai,

Hedden,

Mallick

et al. 2024

Journal of Topology

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Knot Floer homology of satellite knots with (1, 1) patterns

Cited by 1 publication

References 19 publications

Rank‐expanding satellites, Whitehead doubles, and Heegaard Floer homology

Rank‐expanding satellites, Whitehead doubles, and Heegaard Floer homology

Contact Info

Product

Resources

About