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A note on surgery obstructions and hyperbolic integer homology spheres


Authors: Jennifer Hom and Tye Lidman
Journal: Proc. Amer. Math. Soc. 146 (2018), 1363-1365
MSC (2010): Primary 57M29, 57R58
DOI: https://doi.org/10.1090/proc/13925
Published electronically: December 7, 2017
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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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Additional Information

Jennifer Hom
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email: hom@math.gatech.edu

Tye Lidman
Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27607
Email: tlid@math.ncsu.edu

DOI: https://doi.org/10.1090/proc/13925
Received by editor(s): May 4, 2017
Published electronically: December 7, 2017
Additional Notes: The first author was partially supported by NSF grants DMS-1128155, DMS-1307879, DMS-1552285, and a Sloan Research Fellowship.
The second author was supported by NSF grant DMS-1128155.
Communicated by: David Futer
Article copyright: © Copyright 2017 American Mathematical Society

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