Interval-sphere model structures
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916824275222528 |
|---|---|
| author | Hess, Kathryn Lavenir, Samuel Maggs, Kelly |
| author_facet | Hess, Kathryn Lavenir, Samuel Maggs, Kelly |
| contents | The bedrock of persistence theory over a single parameter is decomposition of persistence modules into intervals. In [HLM24], the authors leveraged interval decomposition to produce a cell decomposition of the minimal model of a simply connected copersistent space. The key tool was a technique called interval surgery, which involves the gluing of intervals to a persistent CDGA by means of algebraic cell attachments. In this article, we define a compact, combinatorial model categorical structure that contextualizes interval surgery as a genuine model-categorical cell attachment. We show that our new model structure is neither the injective nor the projective one and that cofibrancy is closely linked to the notion of tameness in persistence theory and algebraic notions of compactness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02382 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interval-sphere model structures Hess, Kathryn Lavenir, Samuel Maggs, Kelly Algebraic Topology 55N31, 55P62, 18N40 The bedrock of persistence theory over a single parameter is decomposition of persistence modules into intervals. In [HLM24], the authors leveraged interval decomposition to produce a cell decomposition of the minimal model of a simply connected copersistent space. The key tool was a technique called interval surgery, which involves the gluing of intervals to a persistent CDGA by means of algebraic cell attachments. In this article, we define a compact, combinatorial model categorical structure that contextualizes interval surgery as a genuine model-categorical cell attachment. We show that our new model structure is neither the injective nor the projective one and that cofibrancy is closely linked to the notion of tameness in persistence theory and algebraic notions of compactness. |
| title | Interval-sphere model structures |
| topic | Algebraic Topology 55N31, 55P62, 18N40 |
| url | https://arxiv.org/abs/2507.02382 |