Polynomial covering spaces and homomorphisms into the braid groups

V. L. (Vagn Lundsgaard) Hansen

Vol. 81 (1979), No. 2, 399–410

DOI: 10.2140/pjm.1979.81.399

Abstract

A polynomial covering space is the zero set for a parametrized family of complex polynomials. Such covering spaces arise naturally in several contexts in the study of holomorphic mappings. There are fruitful connections between polynomial covering spaces and certain homomorphisms into the Artin braid groups. We shall establish these connections and use them to obtain an algebraic classification of the polynomial covering spaces.

Mathematical Subject Classification 2000

Primary: 32C40, 32C40

Secondary: 32H99, 57M05

Milestones

Received: 29 June 1978

Published: 1 April 1979