Rational linking and contact geometry

Kenneth Baker, John Etnyre

Research output: Chapter in Book/Report/Conference proceedingChapter

17 Scopus citations

Abstract

In the note we study Legendrian and transverse knots in rationally null-homologous knot types. In particular, we generalize the standard definitions of self-linking number, Thurston–Bennequin invariant, and rotation number. We then prove a version of Bennequin’s inequality for these knots and classify precisely when the Bennequin bound is sharp for fibered knot types. Finally, we study rational unknots and show that they are weakly Legendrian and transversely simple.

Original languageEnglish (US)
Title of host publicationProgress in Mathematics
PublisherSpringer Basel
Pages19-37
Number of pages19
Volume296
DOIs
StatePublished - Jan 1 2012

Publication series

NameProgress in Mathematics
Volume296
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X

Keywords

  • Contact geometry
  • Legendrian knot
  • Openbook
  • Self-linking
  • Transverse knot

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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  • Cite this

    Baker, K., & Etnyre, J. (2012). Rational linking and contact geometry. In Progress in Mathematics (Vol. 296, pp. 19-37). (Progress in Mathematics; Vol. 296). Springer Basel. https://doi.org/10.1007/978-0-8176-8277-4_2