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Explore the construction and properties of the Morse fundamental group through this 29-minute conference talk from the IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar. Learn how to combinatorially recover the fundamental group of a manifold M from a given Morse-Smale pair, building upon the foundational concept of the Morse fundamental group. Discover how continuation maps provide functoriality and invariance properties for this construction, drawing inspiration from Barraud's "Floer fundamental group" and the widespread applications of continuation maps in symplectic topology. Examine the key differences between this approach and traditional homological methods, gaining insight into advanced techniques in differential topology and symplectic geometry. The presentation, delivered by Salammbo Connolly from Université Paris-Saclay, offers a deep dive into the intersection of Morse theory and fundamental group theory within the context of modern geometric analysis.
