ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 57N35 Venema, Gerard A., Calvin College, Grand Rapids, Michigan USA Representing homology classes of 4-manifolds Theorem 1 If W is a compact, simply connected, PL 4-manifold, then each element of H_{2}(W) can be represented by a compact PL submanifold M ⊂ W such that M consists of a Mazur-like contractible 4-manifold with a single 2-handle attached. A compact contractible PL 4-manifold is Mazur-like if it has a handle decomposition in which there is one 0-handle, no handles of index greater than 2, and the attaching map for the ith 2-handle is homotopic to the loop represented by the ith 1-handle. Theorem 2 If W is a compact, simply connected, PL submanifold of S^{4}, then each element of H_{2}(W) can be represented by a locally flat topological embedding of S^{2}. It should be noted that both Theorems 1 and 2 are false without the hypothesis that W is compact.