Tangent winding numbers and branched mappings

John Robert Quine, Jr.

Vol. 73 (1977), No. 1, 161–167

DOI: 10.2140/pjm.1977.73.161

Abstract

The notion of tangent winding number of a regular closed curve on a compact 2-manifold M is investigated, and related to the notion of obstruction to regular homotopy. The approach is via oriented intersection theory. For N, a 2-manifold with boundary and F : N → M a smooth branched mapping, a theorem is proved relating the total branch point multiplicity of F and the tangent winding number of F|_∂N. The theorem is a generalization of the classical Riemann-Hurwitz theorem.

Mathematical Subject Classification

Primary: 57A05, 57A05

Milestones

Received: 1 October 1976

Published: 1 November 1977