I know that one can take a supersymmetric theory defined on $\mathbb{R}^n$ and topologically twist it by redefining the rotation group of the theory into a mixture of the rotation group and the R-symmetry group. However, what I'm a bit confused about is: what is a topologically twisted index? What does it physically mean? I can't seem to find a definition anywhere. Most papers seem to assume that the reader already knows the definition.