“Barcodes” for Continuous Maps and a Brief Introduction to Alternative Morse Theory

Dan Burghelea ()
Additional contact information
Dan Burghelea: The Ohio State University, Department of Mathematics

Chapter Chapter 14 in Essays on Topology, 2025, pp 289-309 from Springer

Abstract: Abstract This chapter reviews the description of “barcodes” for a continuous real-valued map f : X → ℝ $$f:X\to \mathbb R$$ and explains how to recover the Morse complex of a Morse function from them. In this presentation, the barcodes appear as the support of two vector-space valued maps, one defined on the Euclidean plane ℝ 2 $$\mathbb R^2$$ and the other on the “above diagonal” half plane ℝ + 2 . $$\mathbb R^2_+.$$

Keywords: Morse theory; Barcodes; Algebraic topology; 46M20; 57R19; 55E05; 55N35 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-81414-3_14

Ordering information: This item can be ordered from
http://www.springer.com/9783031814143

DOI: 10.1007/978-3-031-81414-3_14

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().