Vafa's formula and equivariant \(K\)-theory
Let \(X\) be a quasi-smooth hypersurface in weighted projective space defined by a quasi-homogeneous one of degree \(d\). The natural projection restricted over \(X\) gives rise to a Seifert fibration from \(S_ X\) to the weighted projective space. The Euler characteristic of \(S^ 1\)- equivariant \(K\)-theory of \(S_ X\), that is \(\text{rank }K_{S^ 1}^ 0(S_ X)- \text{rank } K_{S^ 1}^ 1(S_ X)\), is equal to an expression which contains a term that has the same form as Vafa's expression of Witten's index.
scientific article; zbMATH DE number 205508