We describe a localization theory for Maslov classes associated with two Lagrangian subbundles in a real symplectic vector bundle and give a definition of the residue of the Maslov classes. We also compute explicitly the residue of the first Maslov class in the case that the non-transversal set of the two Lagrangian subbundles have codimension 1.
Takeshi IZAWA. Katsunori NAKAJIMA. "Residues of Chern-Maslov classes." J. Math. Soc. Japan 57 (1) 21 - 36, January, 2005. https://doi.org/10.2969/jmsj/1160745811