On smoothable surgery for 4–manifolds

Khan, Qayum

doi:10.2140/agt.2007.7.2117

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On smoothable surgery for 4–manifolds

Qayum Khan

Algebraic & Geometric Topology 7 (2007) 2117–2140

DOI: 10.2140/agt.2007.7.2117

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 $*$ –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

References

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/

Volume 7, issue 4 (2007)