On higher rank instantons & the monopole cobordism program

Details On higher rank instantons & the monopole cobordism program On higher rank instantons & the monopole cobordism program

2009-11-26

arxiv.org/abs/0911.5146v1

Mathematics

Differential Geometry

This manuscript fusions the two previous manuscripts "What to expect from U(n) monopoles" and "PU(N) monopoles, higher rank in

Scientific paper

Witten's conjecture suggests that the polynomial invariants of Donaldson are expressible in terms of the Seiberg-Witten invariants if the underlying four-manifold is of simple type. A higher rank version of the Donaldson invariants was introduced by Kronheimer. Before even having been defined, the physicists Mari\~no and Moore had already suggested that there should be a generalisation of Witten's conjecture to this type of invariants. We study a generalisation of the classical cobordism program to the higher rank situation and obtain vanishing results which gives evidence that the generalisation of Witten's conjecture should hold.

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