The space of discrete Morse functions
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917268461453312 |
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| author | Brüggemann, Julian |
| author_facet | Brüggemann, Julian |
| contents | In this work, we introduce a combinatorial-geometric model for the space of discrete Morse functions on any CW complex $X$. We relate this version of a space of discrete Morse functions to the space of cellular filtrations of $X$ and discuss its relationship to various concepts such as smooth Morse theory, Cerf theory, complexes of discrete Morse matchings, and induced merge trees and barcodes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14032 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The space of discrete Morse functions Brüggemann, Julian Algebraic Topology 57Q70 (Primary), 55N31 (Secondary), 52C35 (Secondary) In this work, we introduce a combinatorial-geometric model for the space of discrete Morse functions on any CW complex $X$. We relate this version of a space of discrete Morse functions to the space of cellular filtrations of $X$ and discuss its relationship to various concepts such as smooth Morse theory, Cerf theory, complexes of discrete Morse matchings, and induced merge trees and barcodes. |
| title | The space of discrete Morse functions |
| topic | Algebraic Topology 57Q70 (Primary), 55N31 (Secondary), 52C35 (Secondary) |
| url | https://arxiv.org/abs/2312.14032 |