@inbook{c5e2d0e4d7814a3888f95b4d5fa6f7f4,

title = "Rational linking and contact geometry",

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{\textquoteright}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.",

keywords = "Contact geometry, Legendrian knot, Openbook, Self-linking, Transverse knot",

author = "Kenneth Baker and John Etnyre",

note = "Funding Information: Acknowledgments The first author was partially supported by NSF Grant DMS-0239600. The second author was partially supported by NSF Grants DMS-0239600 and DMS-0804820.",

year = "2012",

doi = "10.1007/978-0-8176-8277-4_2",

language = "English (US)",

series = "Progress in Mathematics",

publisher = "Springer Basel",

pages = "19--37",

booktitle = "Progress in Mathematics",

}