What would be some good, practical references for some of algebraic topology/geometry arguments in McDuff Salamon, Introduction to Symplectic Topology (3rd edition)?
Specifically, a lot of arguments seem to revolve around looking at the algebraic topology of bundles, ranging from (co)homology to characteristic classes. What are good references that explain examples of such calculations in practice, particularly given background in differential Geometry and basic algebraic Topology?
As a concrete example, in Example 7.1.5 there are calculations done for a blow up $X$ of a point in $\mathbb{C}P^{2}$. What would be good references for an explanation of the following?
How is the "homology of $H_{2} (X; \mathbb{Z})$ generated by the class of the exceptional divisor and the class of the fibre"?
What are the intersection numbers of those generators?
Lemma 7.1.1 is cited, which refers to Theorem 2.7.5 and Exercise 2.7.8, which involve computing the first Chern class relating it to the intersection indices of a section or self-intersection number of the exceptional divisor.