A higher homotopic extension of persistent (co)homology

5 Dec 2014 Estanislao Herscovich

Our objective in this article is to show a possibly interesting structure of homotopic nature appearing in persistent (co)homology. Assuming that the filtration of the (say) simplicial set embedded in a finite dimensional vector space induces a multiplicative filtration (which would not be a so harsh hypothesis in our setting) on the dg algebra given by the complex of simplicial cochains, we may use a result by T. Kadeishvili to get a unique (up to noncanonical equivalence) A_infinity-algebra structure on the complete persistent cohomology of the filtered simplicial (or topological) set... (read more)

PDF Abstract
No code implementations yet. Submit your code now

Datasets


  Add Datasets introduced or used in this paper

Results from the Paper


  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.

Methods used in the Paper


METHOD TYPE
🤖 No Methods Found Help the community by adding them if they're not listed; e.g. Deep Residual Learning for Image Recognition uses ResNet