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Pré-Publication, Document De Travail Année : 2022

On homology planes and contractible 4-manifolds

Résumé

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.
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Dates et versions

hal-04370971 , version 1 (03-01-2024)

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  • HAL Id : hal-04370971 , version 1

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Rodolfo Aguilar, Oğuz Şavk. On homology planes and contractible 4-manifolds. 2024. ⟨hal-04370971⟩
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