$PU(N)$ monopoles, higher rank instantons, and the monopole invariants
| dc.creator | Zentner, Raphael | |
| dc.date | 2008-02-29 | |
| dc.date.accessioned | 2026-07-07T09:24:14Z | |
| dc.date.available | 2026-07-07T09:24:14Z | |
| dc.description | A famous conjecture in gauge theory mathematics, attributed to Witten, 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. Mathematicians have sought a proof of the conjecture by means of a `cobordism program' involving $PU(2)$ monopoles. A higher rank version of the Donaldson invariants was recently introduced by Kronheimer. Before being defined, the physicists Mariño and Moore had already suggested that there should be a generalisation of Witten's conjecture to this type of invariants. We adopt a generalisation of the cobordism program to the higher rank situation by studying $PU(N)$ monopoles. We analyse the differences to the $PU(2)$ situation, yielding evidence that a generalisation of Witten's conjecture should hold. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/0803.0025 | |
| dc.identifier | http://arxiv.org/abs/0803.0025 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156021 | |
| dc.subject | Differential Geometry | |
| dc.subject | Geometric Topology | |
| dc.title | $PU(N)$ monopoles, higher rank instantons, and the monopole invariants | |
| dc.type | text |