Before you read the following question, please assume I have no knowledge in algebraic geometry.
Is it possible to define Segre class of a smooth complex vector bundle over a smooth manifold by using Chern-Weil theory? That is, using connection, curvature and invariant polynoimal, etc.
I know the total Segre class of a holomorphic vector bundle over a complex manifold can be defined as the inverse of the total Chern class (of course one can translate the statement into the language of algebraic geometry). But I have never seen the appearance of Segre class in differential geometric setting. On the other hand, I don't know whether saying "we can define the total Segre form by inverting the total Chern form" makes sense or not.