A note on surgery obstructions and hyperbolic integer homology spheres
Jennifer Hom, Tye Lidman
TL;DR
This paper extends previous work by providing infinitely many hyperbolic integer homology spheres, including those with arbitrary JSJ decompositions, using Heegaard Floer homology techniques.
Contribution
It introduces new infinite families of hyperbolic and JSJ-decomposed integer homology spheres not obtainable by knot surgery in S^3.
Findings
Infinitely many hyperbolic integer homology spheres constructed.
Examples with arbitrary JSJ decompositions provided.
Extension of previous results to broader classes of manifolds.
Abstract
Auckly gave two examples of irreducible integer homology spheres (one toroidal and one hyperbolic) which are not surgery on a knot in the three-sphere. Using Heegaard Floer homology, the authors and Karakurt provided infinitely many small Seifert fibered examples. In this note, we extend those results to give infinitely many hyperbolic examples, as well as infinitely many examples with arbitrary JSJ decomposition.
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