I am reading Nekrasov's paper and in page 2 he considers the $G \times T^2$ equivariant cohomology of the (compactified) moduli space $\tilde{M_k}$ of $U(N)$ instantons on $\mathbb{C}^2$. Here $G$ should denote the gauge group $U(N)$. There exists a map $$ p: \tilde{M} \to pt $$ which, apparently is the map collapsing the moduli space to a point. Can I view this as a deformation retraction to a single point? Why do we need to consider this map?
He then considers the quantity
$$ Z(a,\epsilon_1, \epsilon_2, ; q) = \sum_{k=0}^{\infty}q^k \oint_{\tilde{M_k} }1 $$
where $\oint_{\tilde{M_k} }1$ denotes the localization of the pushforward $p_*1$ of $1 \in H_{G\times T^2}^*(\tilde{M}_k)$ which sends the fundamental class $1$ of the equivariant cohomology of the moduli space to the fundamental class of the equivariant cohomology of a point which is isomorphic to $\mathbb{C}[U,\epsilon_1, \epsilon_2]$.
I understand that somewhere here is hidden the Atiyah-Bott localization formula. I know that the rotation group that acts on $\mathbb{C}^2$ inherits its action to moduli space. But what is Nekrasov exactly localizing on the moduli space?
I know how equivariant localization works but I cannot get my head around on how and why Nekrasov localizes $1$ in this case. Any references from a mathematical point of view would be helpful. I know Nakajima's book has some nice information.
