A generalization of Kneser’s conjecture
Charles D. Feustel · Pacific Journal of Mathematics · 1973
Let M be a closed connected 3-manifold such that π 2 (M) = 0. Suppose that πι(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 I "realizing" the group structure above.Our theorem also considers the case when M has boundary and gives an answer to a problem of Neuwirth.1* Introduction* In 1929 H. Kneser stated the following result 1 in [8].THEOREM K. Let M be a closed, connected Z-manifold* Suppose π x {M) is the nontrivial free product of two groups A ι and A 2 .Then there exists an embedding of the 2-sphere in M which separate M into S-submanifolds M 1 and M 2 such that π^M/) -A 3 -for j = 1, 2.