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On the diffeomorphism group of $ S\sp{1}\times S\sp{2}$


Author: A. Hatcher
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
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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 [Enhancements On Off] (What's this?)

  • [1] E. César de Sá and C. Rourke, The homotopy type of homeomorphism groups of $ 3$-manifolds, Bull. Amer. Math. Soc. 1 (1979), 251-254. MR 513752 (80j:57006)
  • [2] A. Hatcher, Homeomorphisms of sufficiently large $ {P^2}$-irreducible $ 3$-manifolds, Topology 15 (1976), 343-348. MR 0420620 (54:8633)
  • [3] -, A proof of the Smale conjecture (to appear).
  • [4] B. Jahren, One-parameter families of spheres in $ 3$-manifolds, Ph.D. thesis, Princeton Univ., Princeton, N. J., 1975.
  • [5] S. Smale, Diffeomorphisms of the $ 2$-sphere, Proc. Amer. Math. Soc. 10 (1959), 621-626. MR 0112149 (22:3004)

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DOI: https://doi.org/10.1090/S0002-9939-1981-0624946-2
Article copyright: © Copyright 1981 American Mathematical Society

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