Vol. 73, No. 1, 1977

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
Other MSP Journals
Tangent winding numbers and branched mappings

John Robert Quine, Jr.

Vol. 73 (1977), No. 1, 161–167

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
Received: 1 October 1976
Published: 1 November 1977
John Robert Quine, Jr.