Fuchsian groups, geodesic flows on surfaces of constant negative curvature and symbolic coding of geodesics. These maps are defined on the unit circle the boundary of the poincar\e disk by the generators of the group and have a finite set of discontinuities. On arithmetic fuchsian groups and their characterisations. The fuchsian results are joint with svetlana katok and build on results of katok and ugarcovici, who studied a family of maps generalizing the bowenseries boundary map. This introductory text provides a thoroughly modern treatment of fuchsian groups that addresses both the classical material and recent developments in the field. Structure of attractors for boundary maps associated to fuchsian. The primary course text will be svetlanas katoks book fuchsian groups. Fuchsian groups on the hyperbolic plane h2, the unit tangent bundle t1h2 and psl2,r and some basic examples of fundamental domain in h2. Assume that the group o1 of units in o with reduced norm equal to 1. The group psl2,r acts on h by linear fractional transformations also known as mobius transformations. Finitely generated fuchsian groups exercises for chapter 4 5. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects.
The fundamental group of a polygonal complex 184 c. We study the two forward orbits of each discontinuity point and show that for a family of such maps the cycle property. We consider the unit disc d z c, izl free delivery worldwide. They are particular instances of arithmetic groups. Climenhagas lectures on surfaces american mathematical society, providence 2008, and s. Discrete subgroup of the real projective special linear group of dimension 2.
We study dynamical properties of generalized bowenseries boundary maps associated to cocompact torsion free fuchsian groups. The idea of schmutz is to consider the free subgroups of 2 generators. Boundary maps and their natural extensions associated with. The most interesting and important ones are the socalled arithmetic fuchsian groups, i. Structure of attractors for boundary maps associated to fuchsian groups. Whether tablehoppingor on stage, performing for three people orvictorian coins and glass is strong, interactive coin magic at its finest. Svetlana katok, fuchsian groups, the university of chicago press, 1992. This action is faithful, and in fact psl2,r is isomorphic to the group of all orientationpreserving. This chapter is an introduction to the planar hyperbolic geometry. Fuchsian groups by svetlana katok, available at book depository with free delivery worldwide. A fuchsian group of the first type is a group for which the limit set is the closed real line r. Reduction theory for fuchsian groups semantic scholar. Factor spaces of the hyperbolic plane 186 lecture 26 wednesday, november 4 188 a. Octipi marked it as toread apr 21, fuchsian groups svetlana katok.
May 09, 2019 elementary mathematics dorofeev potapov download as pdf file. Main fuchsian groups chicago lectures in mathematics. Arithmetic fuchsian groups, quaternion orders, fundamental domains. In this paper we develop a socalled reduction theory for fuchsian groups f. Fuchsian groups, katok the university of chicago press. May, 2020 1992, svetlana katok, fuchsian groups, university of chicago press, page 112, in this chapter we give some examples of fuchsian groups. Watch, ask questions and learn things you wont find in any book or dvd. A very precise, yet intuitive approaach to fuchsian groups.
The book fuchsian groups, svetlana katok is published by university of chicago press. Connection with riemann surfaces and homogeneous spaces 41. Kaneshiro, md, mha, clinical assistant professor of pediatrics, university of washington school of medicine. Fuchsian groups, geodesic flows on surfaces of constant. Definitely recommend it for selfstudy or teaching a first course in hyperbolic geometry. Otherwise, a fuchsian group is said to be of the second type. Pdf on the arithmetic fuchsian groups derived from.
Beardons the geometry of discrete groups springer, new york 1995, a. Jul 27, 2019 fuchsian groups by svetlana katok, available at book depository with free delivery worldwide. Buy fuchsian groups chicago lectures in mathematics on. Fuchsian groups and their fundamental regions 25 7. Fuchsian groups by svetlana katok, 9780226425832, available at book depository with free delivery worldwide. Let ro be the intersection of d with the exteriors of all isometric circles jy.
There is an army regulation army emergency management program. Aug 06, 2019 fuchsian groups, geodesic flows on surfaces of constant negative curvature and symbolic coding of geodesics. Compactness of for fuchsian groups derived from division quaternion algebras 5. Structure of attractors for boundary maps associated to. Jan 11, 2020 fuchsian groups, geodesic flows on surfaces of constant negative curvature and symbolic coding of geodesics. Free products 180 lecture 25 monday, november 2 181 a. Kleinian case, there are no cocompact torsion free examples and we describe the. Jan 22, 2019 fuchsian groups, geodesic flows on surfaces of constant negative curvature and symbolic coding of geodesics. This single location in australian capital territory. Arithmetic fuchsian groups are a special class of fuchsian groups constructed using orders in quaternion algebras.
Jul 14, 2019 katok fuchsian groups pdf fuchsian groups, geodesic flows on surfaces of constant negative curvature and symbolic coding of geodesics. For each g 2, 3, the fuchsian groups so obtained are identi. Apr 19, 2020 fuchsian groups, geodesic flows on surfaces of constant negative curvature and symbolic coding of geodesics. In mathematics, a fuchsian group is a discrete subgroup of psl2,r. Lectures on groups and their connections to geometry anatole. Results 1 14 of 14 elementary mathematics by dorofeev, g. Katok fuchsian groups pdf fuchsian groups, geodesic flows on surfaces of constant negative curvature and symbolic coding of geodesics. Fundamental domains infuchsian groupspsl2 r for arxiv. These groups form a slice in quasifuchsian space, homeomorphic to the teichmulle. The exercises are great and there are hints for the selected ones. Note as an aside addition to the remark about polyhedra not necessarily being nitesided. Buy fuchsian groups chicago lectures in mathematics by svetlana katok isbn. Svetlana katok, fuchsian groups 1992, university of chicago press. These maps are defined on the unit circle the boundary of the poincare disk by the generators of the group and have a finite set of discontinuities.
Ar 52527 pdf ar army emergency management program on free shipping on qualifying offers. A good part of the course will be devoted to developing the techniques to compute explicit examples, using mathematica, sage, and magma. This introductory text provides a thoroughly modern treatment of fuchsian groups that addresses. When the parameters satisfy the short cycle property, i. A basic example of lattices in semisimple groups, fuchsian groups have extensive connections to the theory of a single complex variable, number theory, algebraic and differential geometry, topology, lie theory, representation theory. Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Linear properties of polyfuchsian gr oups 189 nonorientable f uchsian groups, that is, discrete subgroups of. We also give other results on kleinian and fuchsian groups.
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