Similarity Invariants of Essentially normal Cowen-Douglas Operators and Chern Polynomials (1910.10538v1)

Abstract: In this paper, we systematically study a class of essentially normal operators by using the geometry method from the Cowen-Douglas theory and prove a Brown-Douglas-FiLLMore theorem in the Cowen-Douglas theory. More precisely, the Chern polynomials and the second fundamental forms are the similarity invariants (in the sense of Herrero) of this class of essentially normal operators.