Thurston, threedimensional geometry and topology, volume i, edited by silvio levy, princeton mathematical series, 35 1997. Petronio, lectures on hyperbolic geometry, universitext, springer verlag 1991 2 f. Lectures on hyperbolic geometry riccardo benedetti, carlo petronio focussing on the geometry of hyperbolic manifolds, the aim here is to provide an exposition of some fundamental results, while being as selfcontained, complete, detailed and unified as possible. This space is the local model for the class of manifolds we shall deal with in the whole book. Hyperbolic geometry 63 we shall consider in this exposition ve of the most famous of the analytic models of hyperbolic geometry. In mathematics, hyperbolic geometry also called bolyailobachevskian geometry or lobachevskian geometry is a noneuclidean geometry. Lectures on the geometry of manifolds download pdf. Bonaho n l ow dimensional g eometry, new b ook shor tly to app ear. Most importantly, benedetti petronio contains very complete proofs of the mostow rigidity theorem, marguliss lemma, thurstons hyperbolic dehn surgery theorem, and consequences of all these results.
This is the full lecture of a seminar on a new way of thinking about hyperbolic geometry, basically viewing it as relativistic geometry projectivized, that i gave a few years ago at unsw. Everything from geodesics to gaussbonnet, starting with a. Riccardo benedetti carlo petronio lectures on hyperbolic geometry with 175 figures springer. For any given line r and point p not on r, in the plane containing both line r and point p there are at least two distinct lines through p that do not intersect r. Gz zip tgz chapter 2 elliptic and hyperbolic geometry, 926 pdf ps ps. It will be used to construct the model of the hyperbolic plane. Gz zip tgz chapter 3 geometric structures on manifolds, 2743 pdf ps ps. Reliable information about the coronavirus covid19 is available from the world health organization current situation, international travel. Instead, we will develop hyperbolic geometry in a way that emphasises the similarities and more interestingly. Lectures on hyperbolic geometry riccardo benedetti, cario petronio download bok. This is a set of notes from a 5day doityourself or perhaps discoverityourself introduction to hyperbolic geometry. The book concerns the geometry of manifolds and in particular hyperbolic manifolds. Even so, klein saw a fundamental unity in the subject of noneuclidean geometry. A conformal model is one for which the metric is a pointbypoint scaling of the euclidean metric.
The book concerns the geometry of manifolds and in particular. Hyperbolic geometry is projective relativistic geometry. Introduction to hyperbolic geometry 1 topics i geometry of real and complex hyperbolic space models of hyperbolic space. The conjecture uses only the intrinsic geometry of hyperbolic 3space, so it. Numerous and frequentlyupdated resource results are available from this search. Introduction to hyperbolic functions pdf 20 download. Edinburgh lectures on geometry, analysis and physics 5 note that in hyperbolic space we no longer have a notion of \antipodal points. Sorry, we are unable to provide the full text but you may find it at the following locations. This brings us to the second, stronger version of the conjecture. The introduction in the sections of ratcli es book is more systematic.
Hyperbolic 3manifolds math 86500 17462 spring 2012. Lectures on hyperbolic geometry riccardo benedetti, carlo petronio in recent years hyperbolic geometry has been the object and the preparation for extensive study that has produced important and often amazing results and also opened up new questions. The parallel postulate of euclidean geometry is replaced with. In the following two chapters we discuss geometry of circles on the euclidean plane. Chapter 2 for hyperbolic plane and chapter 9 hyperbolic space from the book lowdimensional geometry by francis bonahon. Quantum hyperbolic geometry is a term coined by baseilhac and benedetti,6 to refer to a method for assigning invariants to a 3manifold equipped with a representation of its fundamental group into sl 2c. Lectures on hyperbolic geometry riccardo benedetti. Munkholm, simplices of maximal volume in hyperbolic space, gromovs norm, and gromovs. Petrnoio, springerverlag, 1992 fuchsian groups, by svetlana katok, chicago lectures in mathematics, 1992 references. Diy hyperbolic geometry kathryn mann written for mathcamp 2015 abstract and guide to the reader. It contains several examples and presents in a lecture style.
Lectures iia, and iib are a simpli ed introduction to the work of bonahon, wong and liu. Chapter 1 geometry and threemanifolds with front page, introduction, and table of contents, ivii, 17 pdf ps ps. Bonahon, geometric structures on 3manifolds, handbook of geometric topology, elsevier 2002 3 w. Univ ersit y ma thematics departmen t 197 9, lecture notes. Hyperbolic geometry is a geometry for which we accept the first four axioms of euclidean geometry but negate the fifth postulate, i. Lectures on hyperbolic geometry 1992 edition open library. Benedetti, riccardo benedetti, carlo petronio, 1992, springerverlag edition, in english. Edinburgh lectures on geometry, analysis and physics. Johann bolyai karl gauss nicolai lobachevsky 18021860 17771855 1793. The work described in thurstons lecture notes revolutionized the study of kleinian groups and hyperbolic manifolds, and formed the foundation for parts of thurstons proof of his geometrization theorem.
Although hyperbolic geometry is about 200 years old the work of karl frederich gauss, johann bolyai, and nicolai lobachevsky, this model is only about 100 years old. Bennett is in the department of mathematics at kansas state university. Preface the goal of this book is to present several central topics in geometric group theory,primarilyrelatedtothelargescalegeometryofin. This chapter is devoted to the definition of a riemannian nmanifold. Lectures on hyperbolic geometry by riccardo benedetti,carlo petronio book resume. Oclcs webjunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus. Benedetti petronio also contains a very detailed account of the common beginning of the proof.
Ebooks pdf lectures on hyperbolic geometry universitext. Focussing on the geometry of hyperbolic manifolds, the aim here is to provide an exposition of some fundamental results, while being as selfcontained, complete, detailed and unified as possible. Now here is a much less tangible model of a noneuclidean geometry. Three are conformal models associated with the name of henri poincar e.