Contact surgeries and the transverse invariant in knot Floer homology

Peter Ozsváth; András I. Stipsicz

doi:10.1017/S1474748010000095

Contact surgeries and the transverse invariant in knot Floer homology

Peter Ozsváth
, András I. Stipsicz

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

We study naturality properties of the transverse invariant in knot Floer homology under contact (+1)-surgery. This can be used as a calculational tool for the transverse invariant. As a consequence, we show that the Eliashberg-Chekanov twist knots En are not transversely simple for n odd and n > 3.

Original language	English (US)
Pages (from-to)	601-632
Number of pages	32
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	9
Issue number	3
DOIs	https://doi.org/10.1017/S1474748010000095
State	Published - Jul 2010
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Heegaard Floer homology
Legendrian knots
transverse knots

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10.1017/S1474748010000095

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title = "Contact surgeries and the transverse invariant in knot Floer homology",

abstract = "We study naturality properties of the transverse invariant in knot Floer homology under contact (+1)-surgery. This can be used as a calculational tool for the transverse invariant. As a consequence, we show that the Eliashberg-Chekanov twist knots En are not transversely simple for n odd and n > 3.",

keywords = "Heegaard Floer homology, Legendrian knots, transverse knots",

author = "Peter Ozsv{\'a}th and Stipsicz, \{Andr{\'a}s I.\}",

note = "Funding Information: Acknowledgements. The authors thank Paolo Ghiggini, Andr{\'a}s Juh{\'a}sz, Paolo Lisca, Zolt{\'a}n Szab{\'o} and Dylan Thurston for interesting and helpful discussions. The authors are especially grateful to Sucharit Sarkar for some discussions of naturality. P.S.O. was supported by NSF grants DMS-0505811 and FRG-0244663. A.S. acknowledges support from the Clay Mathematics Institute. A.S. was also partially supported by OTKA T67928 and by the Marie Curie TOK project BudAlgGeo.",

year = "2010",

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doi = "10.1017/S1474748010000095",

language = "English (US)",

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pages = "601--632",

journal = "Journal of the Institute of Mathematics of Jussieu",

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T1 - Contact surgeries and the transverse invariant in knot Floer homology

AU - Ozsváth, Peter

AU - Stipsicz, András I.

N1 - Funding Information: Acknowledgements. The authors thank Paolo Ghiggini, András Juhász, Paolo Lisca, Zoltán Szabó and Dylan Thurston for interesting and helpful discussions. The authors are especially grateful to Sucharit Sarkar for some discussions of naturality. P.S.O. was supported by NSF grants DMS-0505811 and FRG-0244663. A.S. acknowledges support from the Clay Mathematics Institute. A.S. was also partially supported by OTKA T67928 and by the Marie Curie TOK project BudAlgGeo.

PY - 2010/7

Y1 - 2010/7

N2 - We study naturality properties of the transverse invariant in knot Floer homology under contact (+1)-surgery. This can be used as a calculational tool for the transverse invariant. As a consequence, we show that the Eliashberg-Chekanov twist knots En are not transversely simple for n odd and n > 3.

AB - We study naturality properties of the transverse invariant in knot Floer homology under contact (+1)-surgery. This can be used as a calculational tool for the transverse invariant. As a consequence, we show that the Eliashberg-Chekanov twist knots En are not transversely simple for n odd and n > 3.

KW - Heegaard Floer homology

KW - Legendrian knots

KW - transverse knots

UR - https://www.scopus.com/pages/publications/78049231777

UR - https://www.scopus.com/pages/publications/78049231777#tab=citedBy

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M3 - Article

AN - SCOPUS:78049231777

SN - 1474-7480

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SP - 601

EP - 632

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

IS - 3

ER -

Contact surgeries and the transverse invariant in knot Floer homology

Abstract

All Science Journal Classification (ASJC) codes

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