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

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We determine the Lusternik-Schnirelmann (L-S) category of a total space of a sphere-bundle over a sphere in terms of primary 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 a total space N to have the same L-S category as its 'once punctured submanifold' N\{P}, P∈N. Also, necessary and sufficient conditions for a total space M to satisfy Ganea's conjecture are described.

Original languageEnglish
Pages (from-to)701-713
Number of pages13
Issue number3
Publication statusPublished - May 1 2003


All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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