The cohomology of the space of magnetic monopoles. (English) Zbl 0854.57029

The authors’ abstract: “Denote by \(X_q\) the reduced space of \(\text{SU}_2\) monopoles of charge \(q\) in \(\mathbb{R}^3\). In this paper the cohomology of \(X_q\), the cohomology with compact supports of \(X_q\), and the image of the latter in the former are all calculated as representations of \(\mathbb{Z}/q\mathbb{Z}\) which acts on \(X_2\). This provides a nontrivial “lower bound” for the \(L^2\) cohomology of \(X_q\) which is compatible with the conjectures of Sen. It is also shown that, granted some assumptions about the metric on \(X_q\), its \(L^2\) cohomology does not exceed this bound in the situation referred to in the paper as the ‘coprime case’ ”.


57R99 Differential topology
58Z05 Applications of global analysis to the sciences
Full Text: DOI


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