More Brieskorn spheres bounding rational balls

ŞAVK O.

TOPOLOGY AND ITS APPLICATIONS, vol.286, 2020 (SCI-Expanded, Scopus) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 286
  • Publication Date: 2020
  • Doi Number: 10.1016/j.topol.2020.107400
  • Journal Name: TOPOLOGY AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Middle East Technical University Affiliated: No

Abstract

We call an integral homology sphere 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 Sigma(2, 3, 7), Akbulut and Larson recently provided the first infinite families of Brieskorn spheres non-trivially bounding rational homology balls: Sigma(2, 4n + 1, 12n + 5) and Sigma(3, 3n + 1, 12n + 5) for odd n. Using their technique, we present new such families: Sigma(2, 4n + 3, 12n + 7) and Sigma(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. (C) 2020 Elsevier B.V. All rights reserved.