Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Diffeomorphisms of $ 3$-manifolds which are homotopy equivalent to $ S\sp{1}$


Author: L. S. Husch
Journal: Proc. Amer. Math. Soc. 63 (1977), 327-333
MSC: Primary 57A10; Secondary 57D50
DOI: https://doi.org/10.1090/S0002-9939-1977-0448354-1
MathSciNet review: 0448354
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let h be a diffeomorphism of a 3-manifold M which is homotopy equivalent to the 1-sphere. Suppose that the collection of positive iterates of h has compact closure in the space of smooth mappings of M into itself and suppose that this closed set generated by h is not a group. Necessary and sufficient conditions are given that another diffeomorphism g be topologically equivalent to h.


References [Enhancements On Off] (What's this?)

  • [1] C. Ehresmann, Sur les espaces fibrés différentiables, C. R. Acad. Sci. Paris 224 (1947), 1611-1612. MR 8, 595. MR 0020774 (8:595b)
  • [2] M. E. Hamstrom, Homotopy in homeomorphism spaces, TOP and PL, Bull. Amer. Math. Soc. 80 (1974), 207-230. MR 48 # 12581. MR 0334262 (48:12581)
  • [3] L. S. Husch, Diffeomorphisms with convergent iterates, Indiana J. Math. (to appear). MR 0467770 (57:7622)
  • [4] -, Semi-regular actions, Topology Conference, Lecture Notes in Math., vol. 375, Springer-Verlag, Berlin and New York, 1974, pp. 143-148. MR 50 #8481. MR 0356008 (50:8481)
  • [5] L. S. Husch and W. H. Row, One-dimensional polyhedral irregular sets of homeomorphisms of 3-manifolds, Trans. Amer. Math. Soc. 202 (1975), 299-323. MR 51 #9065. MR 0372861 (51:9065)
  • [6] S. Kinoshita, Notes on covering transformation groups, Proc. Amer. Math. Soc. 19 (1968), 421-424. MR 36 #5921. MR 0222871 (36:5921)
  • [7] J. M. Kister, Microbundles are fibre bundles, Ann. of Math. (2) 80 (1964), 190-199. MR 31 #5216. MR 0180986 (31:5216)
  • [8] J. Milnor, Morse theory, Princeton Univ. Press, Princeton, N.J., 1963. MR 29 #634. MR 0163331 (29:634)
  • [9] J. R. Munkres, Elementary differential topology, Princeton Univ. Press, Princeton, N.J., 1963. MR 29 #623. MR 0163320 (29:623)
  • [10] S. P. Novikov, Topology of foliations, Trudy Moskov. Mat. Obšč. 14 (1965), 248-278; English transl., Trans. Moscow Math. Soc. 14 (1967), 268-304. MR 34 #824. MR 0200938 (34:824)
  • [11] A. B. Paalman-de Miranda, Topological semigroups, Mathematisch Centrum, Amsterdam, 1970. (1st ed. 1964; MR 31 # 1663) MR 0167963 (29:5228)
  • [12] J. Stallings, On fibering certain 3-manifolds, Topology of 3-Manifolds and Related Topics (Proc. Univ. of Georgia Inst., 1961), Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 95-100. MR 28 # 1600. MR 0158375 (28:1600)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57A10, 57D50

Retrieve articles in all journals with MSC: 57A10, 57D50


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0448354-1
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society