Morse–Bott theory on posets and a homological Lusternik–Schnirelmann theorem
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.
DOI: 10.1142/S1793525321500709