Normal bundle of a transverse intersection ($\nu (L_1\cap L_2\subset M)\cong \nu (L_1\subset M){|}_{L_1\cap L_2}\oplus \nu (L_2\subset M){|}_{L_1\cap L_2}$)

For a transverse intersection, the quotient map $TM{|}_L\to {\nu }_1{|}_L\oplus {\nu }_2{|}_L$ is onto and has kernel $TL$. This gives the displayed isomorphism of actual normal bundles. Complex structures on the two normal bundles therefore induce a complex structure on the intersection's normal bundle.

// Target: geometry-and-topology.bigb