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Collapsing and essential coverings
the Gromov-Hausdorff convergence Alexandrov spaces Betti numbers
2012/5/25
In the present paper, we consider the family of all compact Alexandrov spaces with curvature bound below having a definite upper diameter bound of a fixed dimension. We introduce the notion of essenti...
Geometrization of postcritically finite branched coverings
Geometrization postcritically finite branched coverings
2010/11/15
We study canonical decompositions of postcritically finite branched coverings of the 2-sphere, as defined by K.~Pilgrim. We show that every hyperbolic cycle in the decomposition does not have a Thurst...