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The Ganea conjecture in proper homotopy via exterior homotopy theory

Published online by Cambridge University Press:  24 March 2010

JOSE M. GARCÍA–CALCINES ,
PEDRO R. GARCÍA–DÍAZ  and
ANICETO MURILLO MAS
JOSE M. GARCÍA–CALCINES
Affiliation:
Departamento de Matemática Fundamental, Universidad de La Laguna, 38271 Islas Canarias, Spain. e-mail: jmgarcal@ull.es, prgdiaz@ull.es
PEDRO R. GARCÍA–DÍAZ
Affiliation:
Departamento de Matemática Fundamental, Universidad de La Laguna, 38271 Islas Canarias, Spain. e-mail: jmgarcal@ull.es, prgdiaz@ull.es
ANICETO 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

In this article we provide sufficient conditions on a space X to verify Ganea conjecture with respect to exterior and proper Lusternik–Schnirelmann category. For this aim we previously develop an exterior version of the Whitehead, cellular approximation, CW-approximation and Blakers–Massey theorems within a homotopy theory of exterior CW-complexes and study their corresponding analogues and consequences in the proper setting.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 149 , Issue 1 , July 2010 , pp. 75 - 91
Copyright
Copyright © Cambridge Philosophical Society 2010

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