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On the Ganea conjecture for manifolds

Author(s): Yu. B. Rudyak
Journal: Proc. Amer. Math. Soc. 125 (1997), 2511-2512.
MSC (1991): Primary 55M30; Secondary 57Q99, 57R19
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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:

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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