On smoothable surgery for 4-manifolds

Details On smoothable surgery for 4-manifolds On smoothable surgery for 4-manifolds

2007-02-04

arxiv.org/abs/math/0702074v6

Algebraic & Geometric Topology, Volume 7 (2007), 2117--2140

Mathematics

Geometric Topology

18 pages, separated into two journal submissions

Scientific paper

Under certain homological hypotheses on a compact 4-manifold, we prove exactness of the topological surgery sequence at the stably smoothable normal invariants. The main examples are the class of finite connected sums of 4-manifolds with certain product geometries. Most of these compact manifolds have non-vanishing second mod 2 homology and have fundamental groups of exponential growth, which are not known to be tractable by Freedman-Quinn topological surgery. Necessarily, the *-construction of certain non-smoothable homotopy equivalences requires surgery on topologically embedded 2-spheres and is not attacked here by transversality and cobordism.

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