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

In: Essays on Topology

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  • Dan Burghelea

    (The Ohio State University, Department of Mathematics)

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 . $$\mathbb R^2_+.$$

Suggested Citation

  • Dan Burghelea, 2025. "“Barcodes” for Continuous Maps and a Brief Introduction to Alternative Morse Theory," Springer Books, in: Louis Funar & Athanase Papadopoulos (ed.), Essays on Topology, chapter 0, pages 289-309, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-81414-3_14
    DOI: 10.1007/978-3-031-81414-3_14
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