A slicing obstruction from the 10/8 theorem

Andrew Donald, Faramarz Vafaee

Published 2015-08-27Version 1

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.