Dehn’s lemma and handle decompositions of some 4-manifolds

Abstract

We give two short proof of a weak version of the theorem of Laudenbach, Poenaru [3]. Also we show that an embedded S1× S2in S4bounds a copy of B2× S2. Finally we establish that if W is a smooth 4-manifold with ∂W = #nS1× S2and W is built from #n-1B2× S2by attaching a 2-handle, then W is homeomorphic to #nB2× S2. © 1980 by Pacific Journal of Mathematics.