The separation conjecture for asymptotic values of small-mass hyperbolic monopoles
The separation conjecture for asymptotic values of small-mass hyperbolic monopoles
Let the parameter space of hyperbolic monopoles contain a compact subset and a disjoint subset, and let the monopoles have sufficiently small mass. Small-mass asymptotic separation conjecture. Given a compact subset and a disjoint subset in the parameter space of monopoles, if the mass is small enough, then the asymptotic values of the corresponding hyperbolic monopoles respectively give two distinct subsets. This would extend the separation result for compact families to situations involving non-compact subsets, such as a point and a deleted neighbourhood. The source presents this as a prospective consequence of the behaviour of well-separated monopoles and gives no resolution.
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Sources & referencesView supporting material
Primary source
Paul Norbury, “Asymptotic values of hyperbolic monopoles”, arXiv:math/9911146 (1999).
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