Discrete Invariants of Quadratic Endomorphisms

摘要

We present a number of results concerned with discrete topological and geometric invariants of quadratic endomorphisms of real vector spaces. The main attention is given to the mapping degree and cardinalities of fibres of proper endomorphism. Concerning topological invariants, we present a general estimate for the mapping degree and verify its exactness in various classes. Next, we introduce several geometric invariants derived from the structure of the singular set and discriminant of endomorphism. For stable quadratic endomorphisms, we also consider an additional invariant arising from the classification of stable singularities. Several related results and conjectures are also discussed.