A generalization of Kneser’s conjecture

C. D. Feustel

Vol. 46 (1973), No. 1, 123–130

DOI: 10.2140/pjm.1973.46.123

Abstract

Let M be a closed connected 3-manifold such that π₂(M) = 0. Suppose that π₁(M) is a nontrivial free product with amalgamation across the group of a closed connected surface S other than the projective plane or 2-sphere. Then it is shown that there is an embedded surface S in M “realizing” the group structure above.

Our theorem also considers the case when M has boundary and gives an answer to a problem of Neuwirth.

Mathematical Subject Classification

Primary: 55A05

Milestones

Received: 24 February 1972

Published: 1 May 1973