A note on surgery obstructions and hyperbolic integer homology spheres. (English) Zbl 1383.57018
Summary: D. Auckly [AMS/IP Stud. Adv. Math. 2, 21–34 (1997; Zbl 0889.57022)] 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 Ç. Karakurt [Geom. Topol. 20, No. 4, 2219–2251 (2016; Zbl 1352.57021)] 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.
MSC:
| 57M27 | Invariants of knots and \(3\)-manifolds (MSC2010) |
| 57R58 | Floer homology |
References:
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