The Ganea conjecture in proper homotopy via exterior homotopy theory

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...

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Bibliographic Details
Published in:Mathematical proceedings of the Cambridge Philosophical Society 2010-07, Vol.149 (1), p.75-91, Article 75
Main Authors: GARCÍA–CALCINES, JOSE M., GARCÍA–DÍAZ, PEDRO R., MURILLO MAS, ANICETO
Format: Article
Language:English
Subjects:
Approximation
Categories
Cellular
Exteriors
Homotopy theory
Mathematical analysis
Mathematics
Theorems
Theory
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Summary: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.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004110000174