What a real function knows about the manifold on which it is defined: a generalization of Morse theory.

by Dr Mihai Damian (University of Strassbourg)

Tuesday 30 Jan 2024, 17:00 → 18:00 Europe/Berlin

H4 (Geomatikum)

Abstract : Given a generic real function f on a closed manifold X  and its gradient V with respect to some generic metric, the classical Morse theory yields a complex which computes the singular homology of X. In a recent joint work with JF. Barraud, V. Humilière and A. Oancea we defined a more general complex using the Morse data (f,V): we call it Morse complex with differential graded coefficients. In this talk I will explain  how we defined it, the significance of its homology in some particular cases, and the applications which motivated our work.