Finiteness of $A_n$-equivalence types of gauge groups

Details Finiteness of $A_n$-equivalence types of gauge groups Finiteness of $A_n$-equivalence types of gauge groups

2011-07-20

arxiv.org/abs/1107.3908v1

Mathematics

Algebraic Topology

17 pages, 10 figures

Scientific paper

Let $B$ be a finite CW complex and $G$ a compact connected Lie group. We show
that the number of gauge groups of principal $G$-bundles over $B$ is finite up
to $A_n$-equivalence for $n<\infty$. As an example, we give a lower bound of
the number of $A_n$-equivalence types of gauge groups of principal
$\SU(2)$-bundles over $S^4$.

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