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

Oğuz Şavk

Oğuz Şavk

CNRS and Laboratorie de Mathématiques Jean Leray, Nantes Université, 44322 Nantes, France

E-mail Address: oguz.savk@cnrs.fr

E-mail Address: oguz.savk@univ-nantes.fr

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https://doi.org/10.1142/S0129167X24500629Cited by:0 (Source: Crossref)

Abstract

A central problem in low-dimensional topology asks which homology three-spheres bound contractible four-manifolds or homology four-balls. In this paper, we address this question for plumbed three-manifolds and we present two new infinite families. We consider most of the classical examples from around the 1980s by reproving that they all bound Mazur manifolds. We also show that several well-known families bound possibly different types of four-manifolds, called Poénaru homology four-balls. To unify classical and new results in a fairly simple way, we modify Mazur’s argument and work with Poénaru manifolds.

Communicated by Jongil Park

Keywords:

AMSC: 57R65

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