On the Ganea conjecture for manifolds
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- by Yu. B. Rudyak PDF
- Proc. Amer. Math. Soc. 125 (1997), 2511-2512 Request permission
Abstract:
Using a result of Singhof, we prove that $\operatorname {cat} (M \times S^ m)=\operatorname {cat} M+1$ provided $M$ is a connected closed PL manifold with $\dim M \leq 2\operatorname {cat} M-3$ and $S^ m$ is the $m$-sphere, $m>0$.References
- Tudor Ganea, Some problems on numerical homotopy invariants, Symposium on Algebraic Topology (Battelle Seattle Res. Center, Seattle Wash., 1971) Lecture Notes in Math., Vol. 249, Springer, Berlin, 1971, pp. 23–30. MR 0339147
- Wilhelm Singhof, Minimal coverings of manifolds with balls, Manuscripta Math. 29 (1979), no. 2-4, 385–415. MR 545050, DOI 10.1007/BF01303636
Additional Information
- Yu. B. Rudyak
- Affiliation: Mathematisches Institut, Universität Heidelberg, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germany
- Email: july@mathi.uni-heidelberg.de
- Received by editor(s): March 7, 1996
- Additional Notes: The author was partially supported by Deutsche Forschungsgemeinschaft
- Communicated by: Thomas Goodwillie
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2511-2512
- MSC (1991): Primary 55M30; Secondary 57Q99, 57R19
- DOI: https://doi.org/10.1090/S0002-9939-97-03982-8
- MathSciNet review: 1402886