Geometry & Topology

Order in the concordance group and Heegaard Floer homology

Stanislav Jabuka and Swatee Naik

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Abstract

We use the Heegaard–Floer homology correction terms defined by Ozsváth–Szabó to formulate a new obstruction for a knot to be of finite order in the smooth concordance group. This obstruction bears a formal resemblance to that of Casson and Gordon but is sensitive to the difference between the smooth versus topological category. As an application we obtain new lower bounds for the concordance order of small crossing knots.

Article information

Source
Geom. Topol., Volume 11, Number 2 (2007), 979-994.

Dates
Received: 20 November 2006
Revised: 6 February 2007
Accepted: 30 January 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799866

Digital Object Identifier
doi:10.2140/gt.2007.11.979

Mathematical Reviews number (MathSciNet)
MR2326940

Zentralblatt MATH identifier
1132.57008

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57R58: Floer homology

Keywords
concordance order Heegaard Floer homology

Citation

Jabuka, Stanislav; Naik, Swatee. Order in the concordance group and Heegaard Floer homology. Geom. Topol. 11 (2007), no. 2, 979--994. doi:10.2140/gt.2007.11.979. https://projecteuclid.org/euclid.gt/1513799866


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References

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