Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 7, Number 4 (2007), 2117-2140.
On smoothable surgery for 4–manifolds
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.
Algebr. Geom. Topol., Volume 7, Number 4 (2007), 2117-2140.
Received: 4 August 2007
Revised: 10 December 2007
Accepted: 12 December 2007
First available in Project Euclid: 20 December 2017
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Khan, Qayum. On smoothable surgery for 4–manifolds. Algebr. Geom. Topol. 7 (2007), no. 4, 2117--2140. doi:10.2140/agt.2007.7.2117. https://projecteuclid.org/euclid.agt/1513796784