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A Whitehead–Ganea approach for proper Lusternik–Schnirelmann category†

Published online by Cambridge University Press:  01 May 2007

J. M. GARCÍA–CALCINES ,
P. R. GARCÍA–DÍAZ  and
A. MURILLO MAS
J. M. GARCÍA–CALCINES
Affiliation:
Departamento de Matemática Fundamental, Universidad de La Laguna, 38271 Islas Canarias, Spain. e-mail: jmgarcal@ull.es, prgdiaz@ull.es
P. R. GARCÍA–DÍAZ
Affiliation:
Departamento de Matemática Fundamental, Universidad de La Laguna, 38271 Islas Canarias, Spain. e-mail: jmgarcal@ull.es, prgdiaz@ull.es
A. MURILLO MAS
Affiliation:
Departamento of Álgebra, Geometría y Topología, Universidad of Málaga, Ap. 59, 29080 Málaga, Spain. e-mail: aniceto@agt.cie.uma.es
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Abstract

We establish Whitehead and Ganea characterizations for proper LS-category. We use the embedding of the proper category into the exterior category, and construct in the latter a suitable closed model structure of Strøm type. Then, from the axiomatic LS-category arising from the exterior homotopy category we can recover the corresponding proper LS invariants. Some applications are given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 3 , May 2007 , pp. 439 - 457
Copyright
Copyright © Cambridge Philosophical Society 2007

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