Reading Atiyah's article

I’m reading Atiyah’s article about his homonymous theorem but cannot figure out some of the notations he used. I’m not very familiar with algebraic geometry, so I thought I could ask here for some help: the article to which I refer is ("Convexity and commuting hamiltonians").

• There, he talks about "Negative normal bundle" (Proof of Lemma 2.1). I know what a normal bundle is, but I don’t know what a negative normal bundle actually is;
• at the very beginning he defined "almost periodic vector fields" as those that generate a torus action (and I didn’t understand in which sense can a vectorial field generate an action (probably by exponential?)); referring to that, in (Lemma 2.2) he said that the almost periodic vector field "$X_phi$ is the set of the fixed points" of the action generated by $X_phi$ (How can a vector field be a set of points?);
• At page 6, he used the following notation: "$pmphi|N$" and "$pm f_{n+1}|N$" where $phi$ and $f_{n+1}$ are real valued functions. What does it mean (he said that $pmphi|N$– for example – has $Zcap N$ as a non-degenerate critical manifold, so I guess they both are subsets of $N$)?