Vol. 73, No. 1, 1977

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Tangent winding numbers and branched mappings

John Robert Quine, Jr.

Vol. 73 (1977), No. 1, 161–167
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
Authors
John Robert Quine, Jr.