A slicing obstruction from the 10/8 theorem
From Furuta's 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.
Additional Information© 2016 American Mathematical Society. Received by the editors October 15, 2015 and, in revised form, November 17, 2015 and November 25, 2015. Article electronically published on August 29, 2016. The authors would like to thank Matthew Hedden, Adam Levine, and Yi Ni for insightful conversations and their interest in our work. The authors would also like to thank Jae Choon Cha, David Krcatovich, and Brendan Owens for helpful discussions and their comments on an earlier draft of this paper. Lastly, they thank the referee for useful comments.
Published - S0002-9939-2016-13056-6.pdf
Submitted - 1508.07047v2.pdf