Gerbes on orbifolds and exotic smooth R**4

Nov, 2009
22 pages
e-Print:

Citations per year

201020112012351
Abstract: (arXiv)
By using the relation between foliations and exotic R^4, orbifold KK-theory deformed by a gerbe can be interpreted as coming from the change in the smoothness of R^4. We give various interpretations of integral 3-rd cohomology classes on S^3 and discuss the difference between large and small exotic R^4. Then we show that KK-theories deformed by gerbes of the Leray orbifold of S^3 are in one-to-one correspondence with some exotic smooth R^4's. The equivalence can be understood in the sense that stable isomorphisms classes of bundle gerbes on S^3, the boundary of the Akbulut cork, correspond uniquely to these exotic R^4's. Given the orbifold SU(2)×SU(2)SU(2)SU(2)\times SU(2)\rightrightarrows SU(2) where SU(2) acts on itself by conjugation, the deformations of the equivariant KK-theory on this orbifold by the elements of HSU(2)3(SU(2),Z)H_{SU(2)}^{3}(SU(2),\mathbb{Z}), correspond to the changes of suitable exotic smooth structures on R^4.
Note:
  • 21 pages, no figures, subm. to Comm. Math. Phys
  • K-theory
  • orbifold
  • cohomology
  • twist
  • SU(2) x SU(2)
  • S(3)
  • R(4)
  • deformation
  • E(8)
  • mathematical methods