Surfaces and Planar Discontinuous Groups (Lecture Notes in Mathematics) - ISBN:3540100245

Surfaces and Planar Discontinuous Groups (Lecture Notes in Mathematics)

Date: 05 June 2011, 01:29

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For the two-dimensional manifolds, the surfaces, the classical topological problems - classification and Hauptvermutung - have long been solved, and more delicate questions can be investigated. However, the most interesting side of surface theory is not the topological, but the analytic. Results of the complex analytic theory, e.g., are often purely topological, but their proofs are not, using deep theorems of function theory. This results from a natural and close connection with discontinuous groups of motions in the non-euclidean or euclidean plane.
The following lectures deal in the first place with combinatorial topological theorems on surfaces and planar discontinuous groups; thus we have adopted the concept of the book "Einfuhrung in die kombinatorische Topologie" by K. Reidemeister.
Admittedly, in chapters 1-5 we have not kept strictly to the combinatorial conception, but have changed to another category where this seems convenient. Thus we are far from striving for the purity of the above book, and e.g. group theoretic theorems are sometimes proved geometrically, and vice versa.

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