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Cannon-Thurston maps for surface groups: an exposition of amalgamation geometry and split geometry. (English) Zbl 1360.57007
Aravinda, C. S. (ed.) et al., Geometry, topology, and dynamics in negative curvature. Proceedings of the ICM 2010 satellite conference, Raman Research Institute, Bangalore, India, August 2–7, 2010. Cambridge: Cambridge University Press (ISBN 978-1-107-52900-7/pbk; 978-1-316-27584-9/ebook). London Mathematical Society Lecture Note Series 425, 221-271 (2016).
Summary: This is an expository paper, aimed at giving a leisurely account of some model geometries associated to surface Kleinian groups. We describe the notion of manifolds of amalgamation geometry and its generalization, split geometry. We show that the limit set of any surface group of split geometry is locally connected, by constructing a natural Cannon-Thurston map.
For the entire collection see [Zbl 1348.53004].

57-02 Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes
57M50 General geometric structures on low-dimensional manifolds
57M05 Fundamental group, presentations, free differential calculus