What to expect from $U(n)$ Seiberg-Witten monopoles for $n > 1$

Details What to expect from $U(n)$ Seiberg-Witten monopoles for $n > 1$ What to expect from $U(n)$ Seiberg-Witten monopoles for $n > 1$

2008-02-29

arxiv.org/abs/0803.0023v1

Mathematics

Differential Geometry

17 pages

Scientific paper

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 K\"ahler surfaces with $b_2^+ > 1$, the moduli spaces become empty as soon as we perturb with a non-vanishing holomorphic 2-form.

Affiliated with

Also associated with

No associations

Rating

What to expect from $U(n)$ Seiberg-Witten monopoles for $n > 1$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with What to expect from $U(n)$ Seiberg-Witten monopoles for $n > 1$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and What to expect from $U(n)$ Seiberg-Witten monopoles for $n > 1$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-559370