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Proceedings of the American Mathematical Society

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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. Tudor Ganea, Some problems on numerical homotopy invariants, Symposium on Algebraic Topology (Battelle Seattle Res. Center, Seattle Wash., 1971) Springer, Berlin, 1971, pp. 23–30. Lecture Notes in Math., Vol. 249. MR 0339147
  • 2. Wilhelm Singhof, Minimal coverings of manifolds with balls, Manuscripta Math. 29 (1979), no. 2-4, 385–415. MR 545050, 10.1007/BF01303636

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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