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arXiv · 0911.5146

On higher rank instantons & the monopole cobordism program

Raphael Zentner
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Abstract

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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Raphael Zentner. 2009-11-26. On higher rank instantons & the monopole cobordism program. https://doi.org/10.1093/qmath/haq035

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