Collapsing 4-manifolds under a lower curvature bound
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2012
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929216198541312 |
|---|---|
| author | Yamaguchi, Takao |
| author_facet | Yamaguchi, Takao |
| contents | In this paper we describe the topology of 4-dimensional closed orientable Riemannian manifolds with a uniform lower bound of sectional curvature and with a uniform upper bound of diameter which collapse to metric spaces of lower dimensions. This enables us to understand the set of homeomorphism classes of closed orientable 4-manifolds with those geometric bounds on curvature and diameter. In the course of the proof of the above results, we obtain the soul theorem for 4-dimensional complete noncompact Alexandrov spaces with nonnegative curvature. A metric classification for 3-dimensional complete Alexandrov spaces with nonnegative curvature is also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1205_0323 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Collapsing 4-manifolds under a lower curvature bound Yamaguchi, Takao Differential Geometry 53C20, 53C23 (Primary) 57N10, 57M99 (Secondary) In this paper we describe the topology of 4-dimensional closed orientable Riemannian manifolds with a uniform lower bound of sectional curvature and with a uniform upper bound of diameter which collapse to metric spaces of lower dimensions. This enables us to understand the set of homeomorphism classes of closed orientable 4-manifolds with those geometric bounds on curvature and diameter. In the course of the proof of the above results, we obtain the soul theorem for 4-dimensional complete noncompact Alexandrov spaces with nonnegative curvature. A metric classification for 3-dimensional complete Alexandrov spaces with nonnegative curvature is also given. |
| title | Collapsing 4-manifolds under a lower curvature bound |
| topic | Differential Geometry 53C20, 53C23 (Primary) 57N10, 57M99 (Secondary) |
| url | https://arxiv.org/abs/1205.0323 |