Distributional category of manifolds
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908336694231040 |
|---|---|
| author | Jauhari, Ekansh |
| author_facet | Jauhari, Ekansh |
| contents | Recently, a new homotopy invariant of metric spaces, called the distributional LS-category, was defined, which provides a lower bound to the classical LS-category. In this paper, we obtain several sufficient conditions for the distributional LS-category (dcat) of a closed manifold to be maximum, i.e., equal to its classical LS-category (cat). These give us many new computations of dcat, especially for some essential manifolds and (generalized) connected sums. In the process, we also determine the cat of closed 3-manifolds having torsion-free fundamental groups and some closed geometrically decomposable 4-manifolds. Finally, we extend some of our results to closed Alexandrov spaces with curvature bounded below and discuss their cat and dcat in dimension 3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11036 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distributional category of manifolds Jauhari, Ekansh Geometric Topology Algebraic Topology 55M30 (Primary) 55S35, 53C23, 57N65, 53D05, 57M10 (Secondary) Recently, a new homotopy invariant of metric spaces, called the distributional LS-category, was defined, which provides a lower bound to the classical LS-category. In this paper, we obtain several sufficient conditions for the distributional LS-category (dcat) of a closed manifold to be maximum, i.e., equal to its classical LS-category (cat). These give us many new computations of dcat, especially for some essential manifolds and (generalized) connected sums. In the process, we also determine the cat of closed 3-manifolds having torsion-free fundamental groups and some closed geometrically decomposable 4-manifolds. Finally, we extend some of our results to closed Alexandrov spaces with curvature bounded below and discuss their cat and dcat in dimension 3. |
| title | Distributional category of manifolds |
| topic | Geometric Topology Algebraic Topology 55M30 (Primary) 55S35, 53C23, 57N65, 53D05, 57M10 (Secondary) |
| url | https://arxiv.org/abs/2408.11036 |