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Oguz Savk

Publications and source records attributed to Oguz Savk.

3 recordsLinked to original sources
arXiv2024

Classical and new plumbed homology spheres bounding contractible manifolds and homology balls

A central problem in low-dimensional topology asks which homology $3$-spheres bound contractible $4$-manifolds or homology $4$-balls. In this paper, we address this question for plumbed $3$-manifolds and we present two new infinite families. We consider most of the classical examples from around the nineteen eighties by reproving that they all bound Mazur manifolds. We also show that several well-known families bound possibly different types of $4$-manifolds, called Poénaru homology $4$-balls. To unify classical and new results in a fairly simple way, we modify Mazur's argument and work with Poénaru manifolds.

math.GT↗
arXiv2020

More Brieskorn spheres bounding rational balls

We call an integral homology sphere $\textit{non-trivially}$ bounds a rational homology ball if it is obstructed from bounding an integral homology ball. After Fintushel and Stern's well-known example $Σ(2,3,7)$, Akbulut and Larson recently provided the first infinite families of Brieskorn spheres non-trivially bounding rational homology balls: $Σ(2,4n+1,12n+5)$ and $Σ(3,3n+1,12n+5)$ for odd~$n$. Using their technique, we present new such families: $Σ(2,4n+3,12n+7)$ and $Σ(3,3n+2,12n+7)$ for even $n$. Also manipulating their main argument, we simply recover some classical results of Akbulut and Kirby, Fickle, Casson and Harer, and Stern about Brieskorn spheres bounding integral homology balls.

math.GT↗