Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 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.

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The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
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The categories of this paper are: eess
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas