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A slicing obstruction from the $ \frac{10}{8}$ theorem


Authors: Andrew Donald and Faramarz Vafaee
Journal: Proc. Amer. Math. Soc. 144 (2016), 5397-5405
MSC (2010): Primary 57M25, 57M27
DOI: https://doi.org/10.1090/proc/13056
Published electronically: August 29, 2016
MathSciNet review: 3556281
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Abstract: From Furuta's $ \frac {10}{8}$ theorem, we derive a smooth slicing obstruction for knots in $ S^3$ using a spin $ 4$-manifold whose boundary is 0-surgery on a knot. We show that this obstruction is able to detect torsion elements in the smooth concordance group and find topologically slice knots which are not smoothly slice.


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Additional Information

Andrew Donald
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: adonald@math.msu.edu

Faramarz Vafaee
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Email: vafaee@caltech.edu

DOI: https://doi.org/10.1090/proc/13056
Received by editor(s): October 15, 2015
Received by editor(s) in revised form: November 17, 2015, and November 25, 2015
Published electronically: August 29, 2016
Communicated by: Martin Scharlemann
Article copyright: © Copyright 2016 American Mathematical Society