"Barcodes" for continuous maps and a brief introduction to Alternative Morse Theory

2023/05/31 by Burghelea, Dan
#55E05 #55N31 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.19828

Abstract

This paper reviews the description of "bar codes" for a continuous real-valued map and explains how to recover the Morse complex of a Morse function from them. In this presentation the bar codes appear as the support of two vector-space valued maps, one defined on the Euclidean plane and the other on the "above diagonal" half plane.

Related

• Barcodes in level and sub level persistence and Morse-Novikov theory
• Topology Of Real And Angle Valued Maps And Graph Representations (A Brief Survey)
• Topology of angle valued maps, bar codes and Jordan blocks
• Graph Representations and Topology of Real and Angle Valued Maps
• Existence and deformability of topological Morse functions