Brieskorn spheres bounding rational balls

Authors:
Selman Akbulut and Kyle Larson

Journal:
Proc. Amer. Math. Soc. **146** (2018), 1817-1824

MSC (2010):
Primary 57R65; Secondary 57M99

DOI:
https://doi.org/10.1090/proc/13828

Published electronically:
October 30, 2017

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Abstract | References | Similar Articles | Additional Information

Abstract: Fintushel and Stern showed that the Brieskorn sphere bounds a rational homology ball, while its non-trivial Rokhlin invariant obstructs it from bounding an integral homology ball. It is known that their argument can be modified to show that the figure-eight knot is rationally slice, and we use this fact to provide the first additional examples of Brieskorn spheres that bound rational homology balls but not integral homology balls: the families and for odd. We also provide handlebody diagrams for a rational homology ball containing a rationally slice disk for the figure-eight knot, as well as for a rational homology ball bounded by . These handle diagrams necessarily contain 3-handles.

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Additional Information

**Selman Akbulut**

Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48823

Email:
akbulut@math.msu.edu

**Kyle Larson**

Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48823

Email:
larson@math.msu.edu

DOI:
https://doi.org/10.1090/proc/13828

Received by editor(s):
April 27, 2017

Received by editor(s) in revised form:
May 16, 2017

Published electronically:
October 30, 2017

Communicated by:
David Futer

Article copyright:
© Copyright 2017
American Mathematical Society