The (2,1)-cable of the figure-eight knot is not smoothly slice

Abstract: We prove that the (2,1)-cable of the figure-eight knot is not smoothly slice by showing that its branched double cover bounds no equivariant homology ball. This answers a forty-year-old question posed by Kawauchi. This is joint work with Irving Dai, Sungkyung Kang, Abhishek Mallick, and Matthew Stoffregen.