Mathematics – Algebraic Topology
Scientific paper
2010-07-12
Mathematics
Algebraic Topology
11 pages
Scientific paper
We introduce a version of Morse theory for posets, based on R. Forman's discrete Morse theory for regular CW-complexes. Our approach provides a new insight into this subject and is inspired in the homotopy theory of finite topological spaces. The homological variant of our theory can be used to study the topology of triangulable homology manifolds by means of their order triangulations.
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