Lusternik-Schnirelmann invariants in proper homotopy theory

R. Ayala, Eladio Domínguez Murillo, Alberto Márquez Pérez and A. Quintero

Vol. 153 (1992), No. 2, 201–215

DOI: 10.2140/pjm.1992.153.201

Abstract

We introduce and study proper homotopy invariants of the Lusternik-Schnirelmann type, p-cat(−), p-Cat(−), and cat 𝜀(−) in the category of T₂-locally compact spaces and proper maps. As an application, ℝⁿ (n≠3) is characterized as (i) the unique open manifold X with p-Cat(X) = 2, or (ii) the unique open manifold with one strong end and p-cat(x) = 2.

Mathematical Subject Classification 2000

Primary: 55P55

Secondary: 55M30

Milestones

Received: 20 August 1990

Revised: 3 June 1991

Published: 1 April 1992