Cobordism properties of certain manifolds M with C(M) g 3 (C(M) is the Lusternik-Schnirelman category of M) are studied (Lemma 1) with an application to "killing" homotopy groups by surgery (Theorem 1*). An »-manifold is a smooth, connected, compact, «-dimensional manifold without boundary. "[ ]" denotes the "greatest integer" function. Theorem 1. If Misa [n/3]-connected n-manifoldwhere «a3 mod 4 then M cobounds the n-sphere Sn.
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