On smoothable surgery for 4-manifolds

Qayum Khan

doi:10.2140/agt.2007.7.2117

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On smoothable surgery for 4-manifolds

Qayum Khan

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Abstract

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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Qayum Khan. 2007-12-02. On smoothable surgery for 4-manifolds. https://doi.org/10.2140/agt.2007.7.2117

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