The stability theorem for persistent homology is a central result in topological data analysis.
While the original formulation of the result concerns the persistence barcodes of ℝ–valued …

When a category CC satisfies certain conditions, we define the notion of rank invariant for
arbitrary poset-indexed functors F: P → CF: P→ C from a category theory perspective. This …

are mathematical in nature, this article will treat the formalities with a light touch and heavy
references, in order to make the subject more accessible to practitioners. See the concluding …

We consider different notions of equivalence for Morse functions on the sphere in the context
of persistent homology and introduce new invariants to study these equivalence classes …

Identifying and representing clusters in time-varying network data is of particular importance
when studying collective behaviors emerging in nature, in mobile device networks or in …

We build a functorial pipeline for persistent homology. The input to this pipeline is a filtered
simplicial complex indexed by any finite metric lattice, and the output is a persistence …

We study the inverse problem for persistent homology: For a fixed simplicial complex K, we
analyze the fiber of the continuous map PH on the space of filters that assigns to a filter f: K→ …

We employ the recent discovery of functoriality for persistent homology to recast the
Persistent Homology Transform of a geometric complex as a cosheaf of combinatorial …

In this paper, we introduce an extension of smoothing on Reeb graphs, which we call
truncated smoothing; this in turn allows us to define a new family of metrics which generalize …

This paper affirms a conjecture of MacPherson—that the derived category of cellular
sheaves is equivalent to the derived category of cellular cosheaves. We give a self …