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

J. Hyam Rubinstein

Vol. 86 (1980), No. 2, 565–569

DOI: 10.2140/pjm.1980.86.565

Abstract

We give two short proof of a weak version of the theorem of Laudenbach, Poenaru [3]. Also we show that an embedded S¹ × S² in S⁴ bounds a copy of B² × S². Finally we establish that if W is a smooth 4-manifold with ∂W = #_nS¹ × S² and W is built from #_n−1B² × S² by attaching a 2-handle, then W is homeomorphic to #_nB² × S².

Mathematical Subject Classification 2000

Primary: 57N99

Secondary: 57M25, 57R65

Milestones

Received: 30 March 1979

Revised: 4 September 1979

Published: 1 February 1980