a question on genus and index

Question

I work in PDE and not trained in algebraic topology. I came across these two terms, namely, the Krasnoleskii genus and the cohomological index. What is the fundamental difference between a Krasnoleskii genus and a cohomological index?. I know the definition of krasnoleskii genus that it is $\inf\{m:\exists h\in C^0(A,\mathbb{R}^m\setminus\{0\}); h(-x)=-h(x)\}$, where $A$ is closed and symmetric. What about cohomological index?. I don't get the geometric version of it.