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Suspension of Ganea fibrations and a Hopf invariant

✍ Scribed by Lucile Vandembroucq

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 135 KB
Volume: 105
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(99)00058-9

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✦ Synopsis

We introduce a sequence of numerical homotopy invariants σ i cat, i ∈ N, which are lower bounds for the Lusternik-Schnirelmann category of a topological space X. We characterize, with dimension restrictions, the behaviour of σ i cat with respect to a cell attachment by means of a Hopf invariant. Furthermore we establish for σ i cat a product formula and deduce a sufficient condition, in terms of the Hopf invariant, for a space X ∪ e p+1 to satisfy the Ganea conjecture, i.e., cat((X ∪ e p+1 ) × S m ) = cat(X ∪ e p+1 ) + 1. This extends a recent result of Strom and a concrete example of this extension is given.

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