TY - JOUR
T1 - Lusternik-Schnirelmann category of a sphere-bundle over a sphere
AU - Iwase, Norio
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2003/5
Y1 - 2003/5
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=0037782079&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0037782079&partnerID=8YFLogxK
U2 - 10.1016/S0040-9383(02)00026-5
DO - 10.1016/S0040-9383(02)00026-5
M3 - Article
AN - SCOPUS:0037782079
VL - 42
SP - 701
EP - 713
JO - Topology
JF - Topology
SN - 0040-9383
IS - 3
ER -