大鹿 健一

© Springer International Publishing AG 2017. In this chapter we survey how the notion of manifold was born, elaborated, and developed, starting from Riemann’s Habilitationsvortrag. We also touch upon the philosophical side of this development.

Let G, H be two Kleinian groups with homeomorphic quotients H-3/G and H-3/H. We assume that G is of divergence type, and consider the Patterson-Sullivan measures of G and H. The measurable rigidity theorem by Sullivan and Tukia says that a measura...

We consider a compact orientable hyperbolic 3-manifold with a compressible boundary. Suppose that we are given a sequence of geometrically finite hyperbolic metrics whose conformal boundary structures at infinity diverge to a projective lamination...

© 2015, Springer Science+Business Media Dordrecht. Let (Formula presented.) be a Heegaard splitting of a closed orientable 3-manifold M (or a bridge decomposition of a link exterior). Consider the subgroup (Formula presented.) of the mapping class...