Volume 10, issue 1 (2010)

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Odd primary homotopy decompositions of gauge groups

Stephen D Theriault

Algebraic & Geometric Topology 10 (2010) 535–564
Abstract

We construct $p$–local decompositions of certain gauge groups when $p$ is an odd prime. Specifically, we decompose $SU\left(n\right)$, $Sp\left(n\right)$ and $Spin\left(n\right)$–gauge groups over simply connected $4$–manifolds and $U\left(n\right)$–gauge groups over compact, orientable Riemann surfaces, given certain restrictions on $n$ that depend on $p$.

Keywords
gauge group, $p$–local, decomposition
Mathematical Subject Classification 2000
Primary: 54C35, 55P35, 55R10
Publication
Revised: 10 December 2009
Accepted: 24 December 2009
Published: 7 March 2010
Authors
 Stephen D Theriault Department of Mathematical Sciences University of Aberdeen Aberdeen AB24 3UE United Kingdom http://www.maths.abdn.ac.uk/~stephen/