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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 within a homotopy theory of exterior CW-complexes and study their corresponding analogues and consequences in the proper setting.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
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