What to expect from $U(n)$ Seiberg-Witten monopoles for $n > 1$
| dc.creator | Zentner, Raphael | |
| dc.date | 2008-02-29 | |
| dc.date.accessioned | 2026-07-07T09:24:13Z | |
| dc.date.available | 2026-07-07T09:24:13Z | |
| dc.description | We study generalisations to the structure groups U(n) of the familiar (abelian) Seiberg-Witten monopole equations on a four-manifold $X$ and their moduli spaces. For $n=1$ one obtains the classical monopole equations. For $n > 1$ our results indicate that there should not be any non-trivial gauge-theoretical invariants which are obtained by the scheme `evaluation of cohomology classes on the fundamental cycle of the moduli space'. For, if $b_2^+$ is positive the moduli space should be `cobordant' to the empty space because we can deform the equations so as the moduli space of the deformed equations is generically empty. Furthermore, on Kähler surfaces with $b_2^+ > 1$, the moduli spaces become empty as soon as we perturb with a non-vanishing holomorphic 2-form. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/0803.0023 | |
| dc.identifier | http://arxiv.org/abs/0803.0023 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156019 | |
| dc.subject | Differential Geometry | |
| dc.subject | Geometric Topology | |
| dc.title | What to expect from $U(n)$ Seiberg-Witten monopoles for $n > 1$ | |
| dc.type | text |