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

Norio Iwase

doi:10.1016/S0040-9383(02)00026-5

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

Norio Iwase

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	701-713
Number of pages	13
Journal	Topology
Volume	42
Issue number	3
DOIs	https://doi.org/10.1016/S0040-9383(02)00026-5
Publication status	Published - May 2003

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.1016/S0040-9383(02)00026-5

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abstract = "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.",

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AB - 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.

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