Vol. 46, No. 1, 1973

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A generalization of Kneser’s conjecture

C. D. Feustel

Vol. 46 (1973), No. 1, 123–130
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
Authors
C. D. Feustel