Homology and K-theory methods for classes of branes wrapping nontrivial cycles

摘要

We apply some methods of homology and K-theory to special classes of branes wrapping homologically nontrivial cycles. We treat the classification of four-geometries in terms of compact stabilizers ( by analogy with Thurston's classification of three-geometries) and derive the K-amenability of Lie groups associated with locally symmetric spaces listed in this case. More complicated examples of T-duality and topology change from fluxes are also considered. We analyse D-branes and fluxes in type II string theory on CP3 x Sigma(g) x T-2 with torsion H-flux and demonstrate in detail the conjectured T- duality to RP7 x X-3 with no flux. In the simple case of X-3 = T-3, T-dualizing the circles reduces to the duality between CP3 x T-2 x T-2 with H-flux and RP7 x T-3 with no flux.