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

We introduce a version of discrete Morse theory for posets. This theory studies the topology of the order complexes K(X) of h-regular posets X from the critical points of admissible matchings on X. Our approach is related to R. Forman's discrete Morse theory for CW-complexes and generalizes For...

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Detalles Bibliográficos
Autor principal: Minian, E.G.
Formato: JOUR
Materias:
Cellular homology
Combinatorial manifolds
Finite topological spaces
Homology manifolds
Morse theory
Posets
Simplicial complexes
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_01668641_v159_n12_p2860_Minian
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario:We introduce a version of discrete Morse theory for posets. This theory studies the topology of the order complexes K(X) of h-regular posets X from the critical points of admissible 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. © 2012 Elsevier B.V.

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