On the diffeomorphism group of $S^{1}\times S^{2}$
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- by A. Hatcher
- Proc. Amer. Math. Soc. 83 (1981), 427-430
- DOI: https://doi.org/10.1090/S0002-9939-1981-0624946-2
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Abstract:
A disjunction technique for families of $2$-spheres in $3$-manifolds is applied to determine the homotopy type of the diffeomorphism group of ${S^1} \times {S^2}$.References
- Eugénia César de Sá and Colin Rourke, The homotopy type of homeomorphisms of $3$-manifolds, Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 1, 251–254. MR 513752, DOI 10.1090/S0273-0979-1979-14574-9
- Allen Hatcher, Homeomorphisms of sufficiently large $P^{2}$-irreducible $3$-manifolds, Topology 15 (1976), no. 4, 343–347. MR 420620, DOI 10.1016/0040-9383(76)90027-6 —, A proof of the Smale conjecture (to appear). B. Jahren, One-parameter families of spheres in $3$-manifolds, Ph.D. thesis, Princeton Univ., Princeton, N. J., 1975.
- Stephen Smale, Diffeomorphisms of the $2$-sphere, Proc. Amer. Math. Soc. 10 (1959), 621–626. MR 112149, DOI 10.1090/S0002-9939-1959-0112149-8
Bibliographic Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 427-430
- MSC: Primary 57R40; Secondary 58D05
- DOI: https://doi.org/10.1090/S0002-9939-1981-0624946-2
- MathSciNet review: 624946