%0 Journal Article
%T Spherical T-Duality and the spherical Fourier-Mukai transform
%A Peter Bouwknegt
%A Jarah Evslin
%A Varghese Mathai
%J Mathematics
%D 2015
%I arXiv
%X In [arxiv:1405.5844], we introduced spherical T-duality, which relates pairs of the form $(P,H)$ consisting of a principal $SU(2)$-bundle $P\rightarrow M$ and a 7-cocycle $H$ on $P$. Intuitively, spherical T-duality exchanges $H$ with the second Chern class $c_2(P)$. Unless $\mathrm{dim}(M)\leq 4$, not all pairs admit spherical T-duals and the spherical T-duals are not always unique. In this paper, we define a canonical spherical Poincare vector bundle $\mathcal P$ on $SU(2)\times SU(2)$ and the spherical Fourier-Mukai transform, which implements a degree shifting isomorphism in K-theory on the trivial $SU(2)$-bundle with trivial 7-flux, and then (partially) generalise it to prove that all spherical T-dualities induce a natural degree-shifting isomorphism on the 7-twisted K-theories of the principal $SU(2)$-bundles when $\mathrm{dim}(M)\leq 4$.
%U http://arxiv.org/abs/1502.04444v2