On homology planes and contractible $4$-manifolds

Rodolfo Aguilar Aguilar; Oğuz Şavk

doi:10.1112/blms.13043

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arXiv · 2210.11739

On homology planes and contractible $4$-manifolds

Rodolfo Aguilar Aguilar·Oğuz Şavk

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Abstract

We call a non-trivial homology sphere a Kirby-Ramanujam sphere if it bounds both a homology plane and a Mazur or Po\'enaru 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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BibTeX RIS

Rodolfo Aguilar Aguilar, Oğuz Şavk. 2022-10-21. On homology planes and contractible $4$-manifolds. https://doi.org/10.1112/blms.13043

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