Geometry of the extreme Kerr black holes
  Geometrical properties of the extreme Kerr black holes in the topological sectors of nonextreme and extreme configurations are studied. We find that the Euler characteristic plays an essential role to distinguish these two kinds of extreme black holes. The relationship between the geometrical properties and the intrinsic thermodynamics are investigated. 
Bin Wang, Ru-Keng Su and P.K.N.Yu