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Type: Artigo
Title: Conley pairs in geometry—Lusternik–Schnirelmann theory and more
Author: Weber, J.
Abstract: Firstly, we wish to motivate that Conley pairs, realized via Salamon's definition (Salamon, 1990), are rather useful building blocks in geometry: Initially we met Conley pairs in an attempt to construct Morse filtrations of free loop spaces (Weber, 2017). From this fell off quite naturally, firstly, an alternative proof (Weber, 2016) of the cell attachment theorem in Morse theory (Milnor, 1963) and, secondly, some ideas (Majer and Weber, 2015) how to try to organize the closures of the unstable manifolds of a Morse–Smale gradient flow as a CW decomposition of the underlying manifold. Relaxing non-degeneracy of critical points to isolatedness we use these Conley pairs to implement the gradient flow proof of the Lusternik–Schnirelmann Theorem (Lusternik and Schnirelmann, 1934) proposed in Bott's survey (Bott, 1982). Secondly, we shall use this opportunity to provide an exposition of Lusternik–Schnirelmann (LS) theory based on thickenings of unstable manifolds via Conley pairs. We shall cover the Lusternik–Schnirelmann Theorem (Lusternik and Schnirelmann, 1934), cuplength, subordination, the LS refined minimax principle, and a variant of the LS category called ambient category
Subject: Conley, Teoria do índice de
Country: Alemanha
Editor: Elsevier
Rights: Fechado
Identifier DOI: 10.1016/j.exmath.2017.10.003
Date Issue: 2019
Appears in Collections:IMECC - Artigos e Outros Documentos

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