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Journal of Topology Advance Access published online on March 3, 2009
Journal of Topology, doi:10.1112/jtopol/jtp002
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© 2009 London Mathematical Society

Handle moves in contact surgery diagrams

Fan Ding and Hansjörg Geiges

Department of Mathematics, Peking University, Beijing 100871, P. R. China, dingfan@math.pku.edu.cn
Mathematisches Institut, Universität zu Köln, Weyertal 86–90, 50931 Köln, Germany, geiges@math.uni-koeln.de


  Abstract

We describe various handle moves in contact surgery diagrams, notably contact analogues of the Kirby moves. As an application of these handle moves, we discuss the classification of loose Legendrian knots. Along the way, we prove a one-to-one correspondence (up to Legendrian isotopy) between long Legendrian knots in 3-space and their completion in the 3-sphere.

Received May 21, 2008.

2000 Mathematics Subject Classification 57R17, 57R65 (primary), 53D10, 57M25 (secondary)

A part of this research was carried out during F. Ding's stay at the Mathematical Institute of the Universität zu Köln. The first author was supported by the National Natural Science Foundation of China (grant no. 10631060). The second author was partially supported by DFG grant GE 1245/1-2 within the framework of the Schwerpunktprogramm 1154 ‘Globale Differentialgeometrie’.


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