Lusternik-Schnirelmann category of a sphere-bundle over a sphere

2002/02/13 by Norio Iwase · 1 citation
Mathematics · #math.AT #msc:55M30 #msc:55P35 #msc:55Q25 #msc:55R35 #msc:55S36

paper · pdf

published as Topology, 42 (2003), 701--713 · 10 pages

arxiv created 2002/02/13 · arxiv updated 2009/11/30

Abstract

A criterion to determine the L-S category of a total space of a sphere-bundle over a sphere is given in terms of homotopy invariants of its characteristic map, and thus providing a complete answer to Ganea's Problem 4. As a result, we obtain a necessary and sufficient condition for such a total space N to have the same L-S category as its `once punctured submanifold' N\smallsetminus\P\, P ∈ N. Also a necessary condition for such a total space M to satisfy Ganea's conjecture is obtained.

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