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- W1916934485 abstract "In the paper we prove the existence of the strict but relative relation between small exotic $mathbb{R}^{4}$ for a fixed radial family of DeMichelis-Freedman type, and cobordism classes of codimension one foliations of $S^{3}$ distinguished by the Godbillon-Vey invariant, $GVin H^{3}(S^{3},mathbb{R})$ (represented by a 3-form). This invariant can be integrated to get the Godbillon-Vey number. For a fixed radial family, we will show that the isotopy classes (invariance w.r.t. small diffeomorphisms or coordinate transformations) of all members in this family are distinguished by the Godbillon-Vey number of the foliation which is equal to the square of the radius of the radial family. The special case of integer Godbillon-Vey invariants $GVin H^{3}(S^{3},mathbb{Z})$ 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 to 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 these domains causes the quantization of electric charge, the effect usually ascribed to the existence of magnetic monopoles." @default.
- W1916934485 created "2016-06-24" @default.
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- W1916934485 date "2009-04-08" @default.
- W1916934485 modified "2023-09-27" @default.
- W1916934485 title "Gerbes, SU(2) WZW models and exotic smooth R^4" @default.
- W1916934485 hasPublicationYear "2009" @default.
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