Volume 7, issue 4 (2007)

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On smoothable surgery for 4–manifolds

Qayum Khan

Algebraic & Geometric Topology 7 (2007) 2117–2140
 arXiv: math/0702074
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 $\ast$–construction of certain non-smoothable homotopy equivalences requires surgery on topologically embedded 2–spheres and is not attacked here by transversality and cobordism.

Keywords
normal invariants, cobordism
Mathematical Subject Classification 2000
Primary: 57R67
Secondary: 57N65, 57N75
Publication
Received: 4 August 2007
Revised: 10 December 2007
Accepted: 12 December 2007
Published: 26 December 2007
Authors
 Qayum Khan Department of Mathematics Vanderbilt University Nashville TN 37240 USA http://www.math.vanderbilt.edu/people/khan/