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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todo:paper_01668641_v159_n12_p2860_Minian2023-10-03T15:04:29Z Some remarks on Morse theory for posets, homological Morse theory and finite manifolds Minian, E.G. Cellular homology Combinatorial manifolds Finite topological spaces Homology manifolds Morse theory Posets Simplicial complexes 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. Fil:Minian, E.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01668641_v159_n12_p2860_Minian |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Cellular homology Combinatorial manifolds Finite topological spaces Homology manifolds Morse theory Posets Simplicial complexes |
| spellingShingle |
Cellular homology Combinatorial manifolds Finite topological spaces Homology manifolds Morse theory Posets Simplicial complexes Minian, E.G. Some remarks on Morse theory for posets, homological Morse theory and finite manifolds |
| topic_facet |
Cellular homology Combinatorial manifolds Finite topological spaces Homology manifolds Morse theory Posets Simplicial complexes |
| description |
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. |
| format |
JOUR |
| author |
Minian, E.G. |
| author_facet |
Minian, E.G. |
| author_sort |
Minian, E.G. |
| title |
Some remarks on Morse theory for posets, homological Morse theory and finite manifolds |
| title_short |
Some remarks on Morse theory for posets, homological Morse theory and finite manifolds |
| title_full |
Some remarks on Morse theory for posets, homological Morse theory and finite manifolds |
| title_fullStr |
Some remarks on Morse theory for posets, homological Morse theory and finite manifolds |
| title_full_unstemmed |
Some remarks on Morse theory for posets, homological Morse theory and finite manifolds |
| title_sort |
some remarks on morse theory for posets, homological morse theory and finite manifolds |
| url |
http://hdl.handle.net/20.500.12110/paper_01668641_v159_n12_p2860_Minian |
| work_keys_str_mv |
AT minianeg someremarksonmorsetheoryforposetshomologicalmorsetheoryandfinitemanifolds |
| _version_ |
1807317411465003008 |