Flypes of closed 3-braids in the standard contact space

Ki Hyoung Ko; Sang Jin Lee

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 1999; 36(1): 51-71

Printed January 1, 1999

Flypes of closed 3-braids in the standard contact space

Ki Hyoung Ko and Sang Jin Lee

Abstract

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Abstract

We classify all conjugacy classes of 3-braids that are related by flypes on representatives. Among them we determine which classes have representatives that admit both $(+)$ and $(-)$-flypes as an effort to search for a potential example of a pair of transversal knots that are topologically isotopic and have the same Bennequin number but are not transversally isotopic.

Keywords: flype, 3-braid, contact structure, transversal knot

MSC numbers: Primary 57M25; Secondary 57M05