The cohomology of the space of magnetic monopoles |
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Authors: | Graeme Segal Alex Selby |
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Institution: | (1) DPMMS, 16 Mill Lane, CB2 1SB Cambridge, England;(2) New Hall, CB3 0DF Cambridge, England |
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Abstract: | Denote byX
q
the reduced space ofSU
2 monopoles of chargeq in 3. In this paper the cohomology ofX
q
, the cohomology with compact supports ofX
q
, and the image of the latter in the former are all calculated as representations of /q which acts onX
2. This provides a non-trivial lower bound for theL
2 cohomology ofX
q
which is compatible with some conjectures of Sen. It is also shown that, granted some assumptions about the metric onX
q
, itsL
2 cohomology does not exceed this bound in the situation referred to in the paper as the coprime case .The work described here was carried out partly at the University of Texas at Austin. |
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Keywords: | |
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