PL Morse theory in low dimensions
| Autor: | Grunert, Romain, Kühnel, Wolfgang, Rote, Günter |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Advances in Geometry 23 (2023), 135-150 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1515/advgeom-2022-0027 |
| Popis: | We discuss a PL analogue of Morse theory for PL manifolds. There are several notions of regular and critical points. A point is homologically regular if the homology does not change when passing through its level, it is strongly regular if the function can serve as one coordinate in a chart. Several criteria for strong regularity are presented. In particular we show that in low dimensions $d \leq 4$ a homologically regular point on a PL $d$-manifold is always strongly regular. Examples show that this fails to hold in higher dimensions $d \geq 5$. One of our constructions involves an 8-vertex embedding of the dunce hat into a polytopal 4-sphere with 8 vertices such that a regular neighborhood is Mazur's contractible 4-manifold. Comment: 24 pages, 3 figures |
| Databáze: | arXiv |
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