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arXiv · 1410.0995

Classical Morse theory revisited I -- Backward $λ$-Lemma and homotopy type

Joa Weber
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Abstract

We introduce two tools, dynamical thickening and flow selectors, to overcome the infamous discontinuity of the gradient flow endpoint map near non-degenerate critical points. More precisely, we interpret the stable fibrations of certain Conley pairs $(N,L)$, established in [2,3], as a dynamical thickening of the stable manifold. As a first application and to illustrate efficiency of the concept we reprove a fundamental theorem of classical Morse theory, Milnor's homotopical cell attachment theorem [1]. Dynamical thickening leads to a conceptually simple and short proof.

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Joa Weber. 2016-01-29. Classical Morse theory revisited I -- Backward $λ$-Lemma and homotopy type. https://doi.org/10.12775/tmna.2016.020

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