On homology planes and contractible $4$-manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866929602588311552 |
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| author | Aguilar, Rodolfo Aguilar Şavk, Oğuz |
| author_facet | Aguilar, Rodolfo Aguilar Şavk, Oğuz |
| contents | We call a non-trivial homology sphere a Kirby-Ramanujam sphere if it bounds both a homology plane and a Mazur or Poénaru manifold. In 1980, Kirby found the first example by proving that the boundary of the Ramanujam surface bounds a Mazur manifold and it has remained a single example since then. By tracing their initial step, we provide the first additional examples and we present three infinite families of Kirby-Ramanujam spheres. Also, we show that one of our families of Kirby-Ramanujam spheres is diffeomorphic to the splice of two certain families of Brieskorn spheres. Since this family of Kirby-Ramanujam spheres bound contractible $4$-manifolds, they lie in the class of the trivial element in the homology cobordism group; however, both splice components are separately linearly independent in that group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_11739 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On homology planes and contractible $4$-manifolds Aguilar, Rodolfo Aguilar Şavk, Oğuz Geometric Topology Algebraic Geometry We call a non-trivial homology sphere a Kirby-Ramanujam sphere if it bounds both a homology plane and a Mazur or Poénaru manifold. In 1980, Kirby found the first example by proving that the boundary of the Ramanujam surface bounds a Mazur manifold and it has remained a single example since then. By tracing their initial step, we provide the first additional examples and we present three infinite families of Kirby-Ramanujam spheres. Also, we show that one of our families of Kirby-Ramanujam spheres is diffeomorphic to the splice of two certain families of Brieskorn spheres. Since this family of Kirby-Ramanujam spheres bound contractible $4$-manifolds, they lie in the class of the trivial element in the homology cobordism group; however, both splice components are separately linearly independent in that group. |
| title | On homology planes and contractible $4$-manifolds |
| topic | Geometric Topology Algebraic Geometry |
| url | https://arxiv.org/abs/2210.11739 |