Abstract
After surveying classical notions of PL topology of the Seventies, we clarify the relation between Morse theory and its discretization by Forman. We show that PL handles theory and discrete Morse theory are equivalent, in the sense that every discrete Morse vector on some PL triangulation is also a PL handle vector, and conversely, every PL handle vector is also a discrete Morse vector on some PL triangulation. It follows that, in dimension up to 7, every discrete Morse vector on some PL triangulation is also a smooth Morse vector; the viceversa is true in all dimensions. This revises and improves a result by Gallais.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 335-368 |
| Number of pages | 34 |
| Journal | Annali della Scuola normale superiore di Pisa - Classe di scienze |
| Volume | 16 |
| Issue number | 2 |
| State | Published - 2016 |
ASJC Scopus subject areas
- Theoretical Computer Science
- Mathematics (miscellaneous)
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Cite this
Benedetti, B. (2016). Smoothing discrete Morse theory. Annali della Scuola normale superiore di Pisa - Classe di scienze, 16(2), 335-368.