Some remarks on Morse theory for posets, homological Morse theory and finite manifolds

MINIAN, ELIAS GABRIEL

TOPOLOGY AND ITS APPLICATIONS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2012 vol. 159 p. 2860 - 2869

0166-8641

We introduce a version of discrete Morse theory for posets. This theory studies the topology of the order complexes $k(X)$ of it h-regular m posets $X$ from the critical points of it admissible m matchings on $X$. Our approach is related to R. Forman´s discrete Morse theory for CW-complexes and generalizes Forman and Chari´s results on the face posets of regular CW-complexes. We also introduce a homological variant of the theory that can be used to study the topology of triangulable homology manifolds by means of their order triangulations.