A complex Lie group is defined in the same way using complex manifolds rather than real ones (example: SL ⁡ ⁡ ( 2 , C ) ), and holomorphic maps. Similarly, using an alternate metric completion of Q , one can define a p -adic Lie group over the p -adic numbers, a topological group which is also an analytic p -adic manifold, such that the group operations are analytic. In particular, each point has a p -adic neighborhood.