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1972•Transactions of the American Mathematical SocietyRequires access

Piecewise Linear Critical Levels and Collapsing

C. Kearton, W. B. R. Lickorish

Open publisher page 12 citations

Abstract

In this paper the idea of collapsing, and the associated idea of handle cancellation, in a piecewise linear manifold are used to produce a version of Morse theory for piecewise linear embeddings. As an application of this it is shown that, if $n > 2$, there exist triangulations of the $n$-ball that are not simplicially collapsible.

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What this paper is about

In this paper the idea of collapsing, and the associated idea of handle cancellation, in a piecewise linear manifold are used to produce a version of Morse theory for piecewise linear embeddings. As an application of this it is shown that, if $n > 2$, there exist triangulations of the $n$-ball that are not simplicially collapsible.

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OpenAlex reports 12 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper the idea of collapsing, and the associated idea of handle cancellation, in a piecewise linear manifold are used to produce a version of Morse theory for piecewise linear embeddings. As an application of this it is shown that, if $n > 2$, there exist triangulations of the $n$-ball that are not simplicially collapsible.

Key concepts: Piecewise linear manifold, Mathematics, Piecewise linear function, Piecewise, Morse code, Morse theory, Ball (mathematics), Pure mathematics

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