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

Donald, Andrew; Vafaee, Faramarz

doi:10.1090/proc/13056

A slicing obstruction from the $\frac {10}{8}$ theorem
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by Andrew Donald and Faramarz Vafaee PDF

Proc. Amer. Math. Soc. 144 (2016), 5397-5405 Request permission

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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