Branched Coverings over $\mathbb C^2$ and the Jacobian Conjecture

G. V. Egorov

M. V. Lomonosov Moscow State University

Abstract: The class of branched coverings over $\mathbb C^2$ traditionally called exotic arouses interest because of its connection with the Jacobian conjecture. In this paper, we construct a series of examples of such coverings; in particular, methods of construction of coverings with arbitrarily many sheets, as well as with unknotted branch curves, are described. In addition, some topological characteristics of these coverings are computed, which allows us to answer some questions about a possible counterexample to the Jacobian conjecture.

UDC: 514.7

Received: 22.12.2003

DOI: 10.4213/mzm98

 English version: Mathematical Notes, 2004, 76:2, 161–169

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