Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-04-08
Physics
High Energy Physics
High Energy Physics - Theory
21 pages, 8 Figures, RevTeX4 stayle, complete revision with many background material, an error in the argumentation was fixed
Scientific paper
In the paper we prove the existence of the strict relation between small exotic smoothness structures on the Euclidean 4-space $\mathbb{R}^{4}$ from the radial family of DeMichelis-Freedman type, and cobordism classes of codimension one foliations of $S^{3}$. Both are distinguished by the Godbillon-Vey invariants, $GV\in H^{3}(S^{3},\mathbb{R})$, of the foliations which are computed from the value of radii of the radial family. The special case of integer Godbillon-Vey invariants $GV\in H^{3}(S^{3},\mathbb{Z})$ is also discussed and is connected to flat $PSL(2,\mathbb{R})-$bundles. Next we relate these distinguished small exotic smooth $\mathbb{R}^{4}$'s with twisted generalized geometries of Hitchin on $TS^{3}\oplus T^{\star}S^{3}$ and abelian gerbes on $S^{3}$. In particular the change of the smoothness on $\mathbb{R}^{4}$ corresponds to the twisting of the generalized geometry by the abelian gerbe. We formulate the localization principle for exotic 4-regions in spacetime and show that the existence of such domains causes the quantization of electric charge, the effect usually ascribed to the existence of magnetic monopoles.
Asselmeyer-Maluga Torsten
Krol Jerzy
No associations
LandOfFree
Abelian gerbes, generalized geometries and exotic R^4 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 Abelian gerbes, generalized geometries and exotic R^4, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Abelian gerbes, generalized geometries and exotic R^4 will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-214162