All Questions
Tagged with discrete-morse-theory at.algebraic-topology
8
questions
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0
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Critical simplices of a discrete gradient vector field
I am currently reading a paper on topological data analysis which includes som discrete Morse theory arguments. I got stuck on a corollary that in the paper I'm reading is described as simply ...
- 11
2
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0
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161
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Isomorphic simplicial complexes are simple-homotopy-equivalent: reference?
Any two isomorphic simplicial complexes are simple-homotopy-equivalent.
This is a fairly simple result, but it is not obvious. Yet I have been surprisingly unable to find it in the literature on ...
- 33.5k
9
votes
1
answer
263
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Smooth Morse function from Forman's discrete Morse function
Let $M$ be a smooth manifold and $K$ a triangulation of $M$, so $K$ is a regular CW-complex and in particular a simplicial complex. Assume that $M$ is compact so $K$ is finite. Let $f\colon K \to \...
- 909
6
votes
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Existence of a perfect discrete Morse function
Let $X$ denote a regular cell structure on a closed (orientable) $n$-manifold (If it helps, the cells are polytopal and the attaching maps are affine).
Recall that a discrete Morse function on this ...
- 1,017
14
votes
2
answers
1k
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Discrete Morse theory: how do zig-zag paths determine homotopy type?
Let $\Delta$ be a simplicial complex (or more generally, a regular CW complex). Let $\mathcal{M}$ be a Morse matching (or equivalently, a discrete Morse function) on $\Delta$.
By Forman's theorems, $...
- 1,569
6
votes
2
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507
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Using Discrete Morse Theory to represent hom classes
In "vanilla" Morse theory, you can construct cycles representing integral homology classes of a smooth manifold from a Morse function on the manifold (by looking at the flow into/out of the critical ...
0
votes
2
answers
535
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Morse matching with 0-cells and (n-1)-cells
Suppose one has a Morse matching (acyclic matching) of a poset $P$ of rank $n$ in which the only unmatched cells are 0-cells and $(n-1)$-cells, the same number $k$ of each one.
If $P$ is connected ...
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4
votes
2
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882
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Discrete Morse theory and existence of minimal complex
A minimal complex is a CW complex whose only cells are the homology cells.
Is there some sort of criterion on CW complexes about existence of minimal complexes?
Actually I am working on a problem ...
- 1,017