An Algebraic Introduction to Persistence
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910112830980096 |
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| author | Bauer, Ulrich Brüstle, Thomas Scoccola, Luis |
| author_facet | Bauer, Ulrich Brüstle, Thomas Scoccola, Luis |
| contents | We introduce persistence with an emphasis on its algebraic foundations, using the representation theory of posets. Linear representations of posets arise in several areas of mathematics, including the representation theory of quivers and finite dimensional algebras, Morse theory and other areas of geometry, as well as topological inference and topological data analysis -- often via persistent homology. In some of these contexts, the category of poset representations of interest admits a metric structure given by the so-called interleaving distance. Persistence studies the algebraic properties of these poset representations and their behavior under perturbations in the interleaving distance. We survey fundamental results in the area and applications to pure and applied mathematics, as well as theoretical challenges and open questions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07022 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Algebraic Introduction to Persistence Bauer, Ulrich Brüstle, Thomas Scoccola, Luis Algebraic Topology Computational Geometry Commutative Algebra Representation Theory We introduce persistence with an emphasis on its algebraic foundations, using the representation theory of posets. Linear representations of posets arise in several areas of mathematics, including the representation theory of quivers and finite dimensional algebras, Morse theory and other areas of geometry, as well as topological inference and topological data analysis -- often via persistent homology. In some of these contexts, the category of poset representations of interest admits a metric structure given by the so-called interleaving distance. Persistence studies the algebraic properties of these poset representations and their behavior under perturbations in the interleaving distance. We survey fundamental results in the area and applications to pure and applied mathematics, as well as theoretical challenges and open questions. |
| title | An Algebraic Introduction to Persistence |
| topic | Algebraic Topology Computational Geometry Commutative Algebra Representation Theory |
| url | https://arxiv.org/abs/2604.07022 |