Morse–Bott theory on posets and a homological Lusternik–Schnirelmann theorem
D. Fernández-Ternero, Enrique Macías-Virgós, David Mosquera-Lois, José Antonio Vilches · Journal of Topology and Analysis · 2021
We develop Morse–Bott theory on posets, generalizing both discrete Morse–Bott theory for regular complexes and Morse theory on posets. Moreover, we prove a Lusternik–Schnirelmann theorem for general matchings on posets, in particular, for Morse–Bott functions.