Dual 2-complexes in 4-manifolds

Abstract

Concerns decompositions of smooth 4-manifolds as the union of two handlebodies, each with handles of index <=2 (``Heegard'' decompositions).Sample result: Two 2-complexes are (up to 2-deformation) dual spines of a Heegard decomposition of the 4-sphere if and only if they satisfy the conclusions of the Alexander-Lefshetz duality theorem ($H_{1}K\simeq H^{2}L$ and $H_{2}K\simeq H^{1}L$).

19 pages, AMSTeX soruce file