Algebraic interleavings of spaces over the classifying space of the circle
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929678102560768 |
|---|---|
| author | Kuribayashi, Katsuhiko Naito, Takahito Wakatsuki, Shun Yamaguchi, Toshihiro |
| author_facet | Kuribayashi, Katsuhiko Naito, Takahito Wakatsuki, Shun Yamaguchi, Toshihiro |
| contents | We bring spaces over the classifying space $BS^1$ of the circle group $S^1$ to persistence theory via the singular cohomology with coefficients in a field. Then, the {\it cohomology} interleaving distance (CohID) between spaces over $BS^1$ is introduced and considered in the category of persistent differential graded modules. In particular, we show that the distance coincides with the {\it interleaving distance in the homotopy category} in the sense of Lanari and Scoccola and the {\it homotopy interleaving distance} in the sense of Blumberg and Lesnick. Moreover, upper and lower bounds of the CohID are investigated with the cup-lengths of spaces over $BS^1$. As a computational example, we explicitly determine the CohID for complex projective spaces by utilizing the bottleneck distance of barcodes associated with the cohomology of the spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09257 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algebraic interleavings of spaces over the classifying space of the circle Kuribayashi, Katsuhiko Naito, Takahito Wakatsuki, Shun Yamaguchi, Toshihiro Algebraic Topology We bring spaces over the classifying space $BS^1$ of the circle group $S^1$ to persistence theory via the singular cohomology with coefficients in a field. Then, the {\it cohomology} interleaving distance (CohID) between spaces over $BS^1$ is introduced and considered in the category of persistent differential graded modules. In particular, we show that the distance coincides with the {\it interleaving distance in the homotopy category} in the sense of Lanari and Scoccola and the {\it homotopy interleaving distance} in the sense of Blumberg and Lesnick. Moreover, upper and lower bounds of the CohID are investigated with the cup-lengths of spaces over $BS^1$. As a computational example, we explicitly determine the CohID for complex projective spaces by utilizing the bottleneck distance of barcodes associated with the cohomology of the spaces. |
| title | Algebraic interleavings of spaces over the classifying space of the circle |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2501.09257 |