Lusternik-Schnirelmann category of a sphere-bundle over a sphere
Iwase, Norio
Original · EN
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{P}, P ∈ N. Also a necessary condition for such a total space M to satisfy Ganea's conjecture is obtained.
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