various harmonic functions. The result for the metric is (putting all charges but $Q_M$ to one) ds\^2 = ds\^2\_[adS\_3]{} + ds\_[E\^5]{}\^2 + Q\_M \[(d’ + d )\^2 + dØ\_2\^2\]. where $\psi'$ has period $4 \pi$. This still represents $adS_3 \xx E^5 \xx S^3$, since the two terms in the square brackets constitute $S^3$ in the coordinate system corresponding to the Hopf fibration. So again in the near-horizon limit nothing has changed by adding a monopole. Reducing along $\psi'$, one obtains the near-horizon limit of $D2\perp NS5$ lying inside a $D6$ brane. Dualizing with respect to two relative transverse coordinates of $D2$ and $D6$ one obtains a configuration of one $NS5$ brane and two $D4$ branes each of them intersecting the $NS5$ brane on a three brane. This configuration can be uplifted to the standard $M5 \perp M5 \perp M5$ in $11d$. The near-horizon geometry of the latter is $adS_3 \xx E^6 \xx S^2$. In the same way the $M2 \perp M2 \perp M2$ solution may be transformed to $M2 \perp M2 \perp M5 \perp M5$ by adding a monopole.

The wave/monopole rule for the standard intersections is summarized in the figure below.

(11,9) (0,0)[(4,1)[$adS_2 \xx S^2$ (d)]{}]{} (2,1)[(0,1)[2]{}]{} (2,1)[(2,1)[4]{}]{} (0,3)[(4,1)[$adS_2 