A slicing obstruction from the 10/8 theorem

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.

8 pages, 5 figures, v2: minor revisions throughout, Proc. Amer. Math. Soc. (2016)

References in corpus (2)

• Floer homology and knot complements
• Concordance homomorphisms from knot Floer homology