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On the Ganea conjecture for manifolds

Author: Yu. B. Rudyak
Journal: Proc. Amer. Math. Soc. 125 (1997), 2511-2512
MSC (1991): Primary 55M30; Secondary 57Q99, 57R19
MathSciNet review: 1402886
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Abstract: Using a result of Singhof, we prove that $\operatorname {cat}(M \times S\sp m)=\operatorname {cat}M+1$ provided $M$ is a connected closed PL manifold with $\dim M \leq 2\operatorname {cat}M-3$ and $S\sp m$ is the $m$-sphere, $m>0$.

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

  • 1. T. Ganea, Some problems on numerical homotopy invariants, Symposium in Algebraic Topology, Seattle 1971, Edited by P. Hilton (Lect. Notes in Math., vol. 249), Berlin Heidelberg New York: Springer, 1971, pp. 23-30. MR 49:3910
  • 2. W. Singhof, Minimal coverings of manifolds with balls, Manuscripta Math. 29 (1979), 385-415. MR 80k:55012

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Additional Information

Yu. B. Rudyak
Affiliation: Mathematisches Institut, Universität Heidelberg, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germany

Received by editor(s): March 7, 1996
Additional Notes: The author was partially supported by Deutsche Forschungsgemeinschaft
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1997 American Mathematical Society

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