On Hodge Laplacians on General Simplicial Complexes
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_ | 1866909732010196992 |
|---|---|
| author | Bartmann, Philipp Keller, Matthias |
| author_facet | Bartmann, Philipp Keller, Matthias |
| contents | We study Laplacians on general countable weighted simplicial complexes from a conceptual point of view. These operators will first be introduced formally before showing that those formal operators coincide with self-adjoint realizations of operators arising from quadratic forms. A major conceptual perspective is the correspondence to signed Schrödinger operators unveiling the Forman curvature. The main results are criteria for essential self-adjointness via lower bounded Forman curvature and a Gaffney type result via completeness. Finally, we study spectral relations between these Laplacians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07761 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Hodge Laplacians on General Simplicial Complexes Bartmann, Philipp Keller, Matthias Functional Analysis Metric Geometry We study Laplacians on general countable weighted simplicial complexes from a conceptual point of view. These operators will first be introduced formally before showing that those formal operators coincide with self-adjoint realizations of operators arising from quadratic forms. A major conceptual perspective is the correspondence to signed Schrödinger operators unveiling the Forman curvature. The main results are criteria for essential self-adjointness via lower bounded Forman curvature and a Gaffney type result via completeness. Finally, we study spectral relations between these Laplacians. |
| title | On Hodge Laplacians on General Simplicial Complexes |
| topic | Functional Analysis Metric Geometry |
| url | https://arxiv.org/abs/2508.07761 |