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This chapter reviews the description of “barcodes” for a continuous real-valued map \(f :X\to \mathbb R\) 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 \(\mathbb R^2\) and the other on the “above diagonal” half plane \(\mathbb R^2_+.\)

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

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  • 发表日期：

    2025年

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  • Dan Burghelea

摘要

This chapter reviews the description of “barcodes” for a continuous real-valued map \(f :X\to \mathbb R\) 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 \(\mathbb R^2\) and the other on the “above diagonal” half plane \(\mathbb R^2_+.\)