Isotropic classes and Maslov classes (Q1815283)

This paper gives general and detailed construction of the characteristic classes for pairs of isotropic subbundles in a symplectic vector bundle, without flatness condition. One of the main results is as follows: Let \(I_1\) and \(I_2\) be isotropic oriented subbundles of a symplectic vector bundle \(E\to M\). Assume \(\text{rank} I_1 \leq\text{rank} I_2\), and \(I_1\) and \(I_2\) are contained in the Lagrange subbundles \(L_1\) and \(L_2\) of \(E\to M\) respectively. Then each isotropic characteristic class of \((I_1,I_2)\) depends only on the Maslov class of \((L_1, L_2)\) and the Pontryagin class of \(I_1\). Also the explicit formula for the isotropic class is given.