On Transverse Knots and Branched Covers |
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| Authors: | Harvey Shelly; Kawamuro Keiko; Plamenevskaya Olga |
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| Institution: | 1 Department of Mathematics, Rice University, Houston, TX 77005, USA
2 Deparment of Mathematics, Stony Brook University, Stony Brook, NY 11790, USA |
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| Abstract: | We study contact manifolds that arise as cyclic branched coversof transverse knots in the standard contact 3-sphere. We discussproperties of these contact manifolds and describe them in termsof open books and contact surgeries. In many cases we show thatsuch branched covers are contactomorphic for smoothly isotopictransverse knots with the same self-linking number. These pairsof knots include most of the nontransversely simple knots ofBirman–Menasco and Ng–Ozsváth–Thurston. |
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