The space of Fredholm operators classifies $K$-theory. Thus, any continuous family of elliptic operators $(D_x)_{x\in X}$ canonically defines an element in the Abelian group $K(X)$. When $X$ consists of a single point, then one can canonically identify $K(\{x_0\})$ with the group of integers.

The space of Fredholm operators classifies $K$-theory. Thus, any continuous family of elliptic operators $(D_x)_{x\in X}$ canonically defines an element in the Abelian group $K(X)$. When $X$ consists of a single point $x_0$, then one can canonically identify $K(\{x_0\})$ with the group of integers.

The space of Fredholm operators classifies $K$-theory. Thus, any continuous family of elliptic operators $(D_x)_{x\in X}$ canonically defines an element in the Abelian group $K(X)$. When $X$ consists of a singgle point, then one can canonically identify $K(\{x_0\})$ with the group of integers.

The space of Fredholm operators classifies $K$-theory. Thus, any continuous family of elliptic operators $(D_x)_{x\in X}$ canonically defines an element in the Abelian group $K(X)$. When $X$ consists of a single point, then one can canonically identify $K(\{x_0\})$ with the group of integers.