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• W3123507984 abstract "Abstract As shown by Gluck in 1962, the diffeotopy group of S 1 × S 2 is isomorphic to ℤ 2 ⊕ℤ 2 ⊕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 × 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 × S 2 #S 1 × 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)." @default.
• W3123507984 created "2021-02-01" @default.
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• W3123507984 date "2010-03-18" @default.
• W3123507984 modified "2023-09-25" @default.
• W3123507984 title "The diffeotopy group of S1×S2 via contact topology" @default.
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• W3123507984 doi "https://doi.org/10.1112/s0010437x09004606" @default.
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