Work

Fundamental group in stable Morse theory

Year: 2024

Type: dissertation

Abstract: Morse theory relates algebraic topology invariants and the dynamics of the gradient flow of a Morse function, allowing to derive information about one out of the other. In the case of the homology, the construction extends to much more general settings, and in particular to the infinite dimensional setting of the celebrated Floer homology in symplectic geometry. The case of the fundamental group is quiet different however, and the object of this paper is to provide a dynamical description of the fundamental group in the stable Morse setting, which can be thought of as an intermediate case between the Morse and the Floer settings.

Source: Thèses en ligne de l'Université Toulouse III (Université Toulouse III)

DOI: 10.48550/arxiv.2410.07802

Authors: Barraud, Jean-François, Bertuol, Florian

Institutions: Université Toulouse III - Paul Sabatier, Institut National des Sciences Appliquées de Toulouse, Université de Toulouse, Institut de Mathématiques de Toulouse

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4393368532

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