Questions tagged [discrete-morse-theory]

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 ...

If $X$ is a smooth projective toric variety and $P \subset \mathbf{R}^n$ is its moment polytope, then a generic linear function on $\mathbf{R}^n$ induces (1) a Morse function on $X$, and (2) a ...

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 ...

Let's say I have a finite simplicial complex $X$ with a finite covering map $\pi: \widetilde{X} \rightarrow X$ and a discrete gradient vector field $V$ on $X$ (which for my purposes I prefer to its ...

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 ...

I am studying discrete Morse theory and as an example, discrete Morse theory is used to obtain the homotopy type of the complex of non-connected graphs of $n$ vertices. I also read that this kind of ...