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

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

2002-02-13

arxiv.org/abs/math/0202120v1

Topology, 42 (2003), 701--713

Mathematics

Algebraic Topology

10 pages

Scientific paper

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' $N\smallsetminus\{P\}$, $P \in N$. Also a necessary condition for such a total space $M$ to satisfy Ganea's conjecture is obtained.

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