Immersions of surfaces with boundary into the plane

Minoru Yamamoto

Vol. 212 (2003), No. 2, 371–376

DOI: 10.2140/pjm.2003.212.371

Abstract

Let f : M→R² be a smooth immersion of a compact connected oriented surface with boundary M into R². Kauffman defined an equivalence relation called image homotopy and classified the set of all orientation preserving immersions of M into R² up to image homotopy. When M is of genus one and the number of boundary components is strictly greater than one, Kauffman’s result requires a correction. In this paper we will study this particular case.

Milestones

Received: 20 November 2000

Revised: 8 May 2002

Published: 1 December 2003