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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An infinite family of manifolds
with bounded total curvature


Author: A. N. Dranishnikov
Journal: Proc. Amer. Math. Soc. 128 (2000), 255-260
MSC (1991): Primary 53C22; Secondary 53C42, 57C42
Published electronically: May 6, 1999
MathSciNet review: 1618658
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Abstract: The negative answer to the following problem of V. I. Arnold is given: Is the number of topologically different $k$-manifolds of bounded total curvature finite?


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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: http://dx.doi.org/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
Published electronically: May 6, 1999
Additional Notes: The author was partially supported by NSF grant DMS-9500875.
Communicated by: James E. West
Article copyright: © Copyright 1999 American Mathematical Society