1
$\begingroup$

Let $M$ be a submanifold of the Euclidean space $\mathbb{R}^n$. Let $G$ be a finite group acting on $M$ freely. I want to compute the homology (or even the cohomology ring) of $M/G$.

Suppose the coordinates of all points in $M$ are given by some polynomial equations (or inequalities) of the $n$-variables of coordinates of $\mathbb{R}^n$. And the free $G$-action on $M$ is also given by polynomial equations of the $n$-variables of coordinates of $\mathbb{R}^n$. Could we use persistent homology and computer programming codes to compute the homology of $M/G$?

How to do it? Are there any programmes or codes that can be applied?

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.