## Algebraic & Geometric Topology

### On smoothable surgery for 4–manifolds

Qayum Khan

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 7, Number 4 (2007), 2117-2140.

Dates
Revised: 10 December 2007
Accepted: 12 December 2007
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796784

Digital Object Identifier
doi:10.2140/agt.2007.7.2117

Mathematical Reviews number (MathSciNet)
MR2366189

Zentralblatt MATH identifier
1133.57020

Keywords
normal invariants cobordism

#### Citation

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

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