Glättungen von Abbildungen 3-dimensionaler Mannigfaltigkeiten

Harald Boehme

Vol. 61 (1975), No. 1, 45–51

DOI: 10.2140/pjm.1975.61.45

Abstract

Let N and M be compact 3-dimensional manifolds, f : N → M a map. Furthermore let given a Heegaard splitting for M, which certainly exists if M is closed, and then it is a pair (V,W), where V , W are handlebodies (possibly non orientable) with M = V ∪ W, V ∩ W = ∂V = ∂W. It will be shown, that f can be deformed into a normal form with respect to the Heegaard splitting of M: either f has the absolute degree 0, or f is homotopic to a map g with the property that g∣g⁻¹(V ) is a covering map.

Mathematical Subject Classification

Primary: 57A15, 57A15

Milestones

Received: 25 July 1974

Published: 1 November 1975