Piecewise linear critical levels and collapsing

Kearton, C.; Lickorish, W. B. R.

doi:10.1090/S0002-9947-1972-0310899-2

Piecewise linear critical levels and collapsing
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by C. Kearton and W. B. R. Lickorish

Trans. Amer. Math. Soc. 170 (1972), 415-424

DOI: https://doi.org/10.1090/S0002-9947-1972-0310899-2

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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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