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	The diffeotopy group of S-1 x S-2 via contact topology
	Ding, Fan ; Geiges, Hansjoerg
	2010
关键词	diffeotopy group contact topology Legendrian knot LEGENDRIAN KNOTS 3-MANIFOLDS INVARIANTS ISOTOPIES MANIFOLDS HOMOLOGY SPACES LINKS
英文摘要	As shown by Gluck in 1962, the diffeotopy group of S-1 x S-2 is isomorphic to Z(2) circle plus Z(2) circle plus Z(2). Here an alternative proof of this result is given, relying on contact topology. We then discuss two applications to contact topology: (i) it is shown that the fundamental group of the space of contact structures on S-1 x S-2, based at the standard tight contact structure, is isomorphic to Z; (ii) inspired by previous work of Fraser, an example is given of an integer family of Legendrian knots in S-1 x S-2#S-1 x S-2 (with its standard tight contact structure) that can be distinguished with the help of contact surgery, but not by the classical invariants (topological knot type, Thurston-Bennequin invariant, and rotation number).; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000280156000012&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Mathematics; SCI(E); 7; ARTICLE; 4; 1096-1112; 146
语种	英语
出处	SCI
出版者	compositio mathematica
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/314472]
专题	数学科学学院
推荐引用方式 GB/T 7714	Ding, Fan,Geiges, Hansjoerg. The diffeotopy group of S-1 x S-2 via contact topology. 2010-01-01.

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