All Questions

I am completely new to topological data analysis, so I apologise if this is a well-known area of persistent homology, as well as for any imprecise language. Suppose we know completely the topological ...

(I have asked this question at math stackexchange, it was upvoted but got no answers; maybe you can help.) It is well-known that $\beta_1(R(f))\le\beta_1(X)$, where $\beta_1$ is the first Betti ...

Consider a pair of piecewise-linear cobordant $n$ dimensional polyhedra $P_1, P_2$ sitting in $\mathbb{R}^{n+2}$ (with some fixed orientation). Let $O$ be an $n+1$ dimensional piecewise-linear ...

Let $\Omega$ be a regular, finite, $n$-dimensional CW complex with chain modules $\mathscr{C}_k$ and boundary operators $\partial_k$. For many problems in computational geometry, a key operation is to ...

Suppose we have a compact $m$-dimensional submanifold $M$ of $\mathbb{R}^N$ and we want to know the cohomology ring $H^*(M;\mathbb{Z})$. Let $\epsilon>0$ and a $m$-dimensional finite simplicial ...