Barcodes in level and sub level persistence and Morse-Novikov theory

TL;DR

This paper explores the connections between barcodes in level and sub-level persistence and the Morse-Novikov complex for Morse maps, clarifying their relationships and making implicit results explicit.

Contribution

It explicitly relates barcodes in persistence to Morse-Novikov theory, clarifying their connections and making implicit results accessible.

Findings

Relations between barcodes and Morse-Novikov complex clarified

Explicit formulas connecting persistence barcodes with Morse-Novikov theory

Results previously implicit are now clearly stated

Abstract

In this note we recall the relations between the barcodes in level and sub-level persistence and make precise their relation with the Morse-Novikov complex of a Morse real- or angle-valued map. The results in this papers are implicit in my previous work(w.collaborators), but apparently not well known even to experts.