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An infinite family of manifolds with bounded total curvature
Author(s):
A.
N.
Dranishnikov
Journal:
Proc. Amer. Math. Soc.
128
(2000),
255-260.
MSC (1991):
Primary 53C22;
Secondary 53C42, 57C42
Posted:
May 6, 1999
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Abstract:
The negative answer to the following problem of V. I. Arnold is given: Is the number of topologically different  -manifolds of bounded total curvature finite?
References:
- [Ar]
- V. I. Arnold, Dynamics of complexity of intersections, Bol. Soc. Bras. Mat. 2:1 (1990), 1-10. MR 93c:58031
- [Or]
- P. Orlik, Seifert manifolds (Lecture Notes in Math. 291), Springer-Verlag, Berlin, Heidelberg, New York, 1972. MR 54:13950
- [D-N-F]
- B. A. Dubrovin, S. P. Novikov, A. T. Fomenko, Modern geometry (in Russian), vol. 1, Nauka, Moscow, 1979. MR 81f:53001
- [H]
- M. W. Hirsch, Differential topology, Springer-Verlag, New York, Heidelberg, Berlin, 1976. MR 56:6669
- [N-K]
- K. Nomizu, Sh. Kobayashi, Foundations of differential geometry,vol.2, Interscience publishers, New York, London, Sydney, 1969. MR 38:6501
- [R]
- D. Rolfsen, Knots and Links, Publish or Perish, Berkeley, 1976. MR 58:24236; MR 95c:57018
- [A-M]
- S. Akbulut and J. D. McCarty, Casson's invariant for oriented homology 3-spheres: an exposition, Univ. Press, Princeton, 1990. MR 90k:57017
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Additional Information:
A.
N.
Dranishnikov
Affiliation:
Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, Florida 32611-8105
Email:
dranish@math.ufl.edu
DOI:
10.1090/S0002-9939-99-04958-8
PII:
S 0002-9939(99)04958-8
Keywords:
Total curvature,
immersion,
Casson invariant,
Dehn surgery,
Seifert manifold
Received by editor(s):
December 26, 1992
Received by editor(s) in revised form:
March 24, 1998
Posted:
May 6, 1999
Additional Notes:
The author was partially supported by NSF grant DMS-9500875.
Communicated by:
James E. West
Copyright of article:
Copyright
1999,
American Mathematical Society
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