Three are conformal models associated with the name of henri poincar e. But geometry is concerned about the metric, the way things are measured. Riccardo benedetti and carlo petronio, lectures on hyperbolic geometry, universitext, springerverlag, berlin, 1992. Lectures on hyperbolic geometry riccardo benedetti, carlo. Hyperbolic geometry 63 we shall consider in this exposition. Lectures on hyperbolic geometry by riccardo benedetti, 9783540555346, available at book depository with free delivery worldwide.
Albert einsteins special theory of relativity is based on hyperbolic. Benedetti petronio lectures on hyperbolic geometry pdf. Hyperbolic geometry is a noneuclidean geometry where the first four axioms of euclidean geometry are kept but the fifth axiom, the parallel postulate, is changed. Reviews benedetti petronio lectures on hyperbolic geometry pdf is best in online store. Most importantly, benedettipetronio contains very complete proofs of the mostow rigidity theorem, marguliss lemma, thurstons hyperbolic dehn surgery. Three are conformal models associated with the name of henri poincar. Hyperbolic geometry 63 we shall consider in this exposition ve of the most famous of the analytic models of hyperbolic geometry.
Lowdimensional geometry by francis bonahon, ams, isbn 9780821848166 3. Ratcli e, springerverlag gtm 149, isbn 038794348x 4. Page 2 mt5830 about this course hyperbolic geometry is a beautiful subject which blends ideas from algebra, analysis and geometry. Lectures on hyperbolic geometry riccardo benedetti, cario petronio download bok. Petronio, universitext, springerverlag, 1991 foundations of hyperbolic manifolds, j. Calegari, foliations and the geometry of 3manifolds, oxford university press 2007. Petronio, lectures on hyperbolic geometry, universitext, springer verlag 1991 2 f. Hyperbolic geometry in two and three dimensions abstract.
Hyperbolic 3manifolds math 86500 17462 spring 2012. Lectures on the geometry of manifolds download pdf. When the values of the masses are sufficiently large and the cone points are suitably spaced, the distinguished deformations of hyperbolic suspensions determine a relevant open subset of the full parameter space. In order to do that, some time is spent on neutral geometry as well as euclidean geometry. Lectures on the geometry of manifolds download pdfepub. Introduction to hyperbolic geometry 1 topics i geometry of real and complex hyperbolic space models of hyperbolic space. Riccardo benedetti carlo petronio lectures on hyperbolic geometry with 175 figures springer.
Introduction to hyperbolic geometry 1 topics 2 bibliography. In this course we will study interactions between the geometry of the group, topology and algebra. Lectures on hyperbolic geometry by riccardo benedetti,carlo petronio book resume. Volumes have been written on noneuclidean geometry, which the reader must consult for more exhaustive information. Pdf basic facts on hyperbolic geometry and its applications. Lectures on hyperbolic geometry edition 1 available in paperback. A conformal model is one for which the metric is a pointbypoint scaling of the euclidean metric. Time and location description prerequisites organization.
Mathematics 9 classical geometry and lowdimensional. However, formatting rules can vary widely between applications and fields of interest or study. Euclidean geometry is usually the most convenient to describe the physical world surrounding us. Chapter 2 for hyperbolic plane and chapter 9 hyperbolic space from the book lowdimensional geometry by francis bonahon. The fifth axiom of hyperbolic geometry says that given a line l and a point p not on that line, there are at least two lines passing through p that are parallel to l. Lectures on hyperbolic geometry by riccardo benedetti, 9783540555346, available at book. 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. At this point the hyperboloid model is introduced, related to the other models visited, and developed using some concepts from physics as aids. You could go on to al mardens outer circles or benedetti and petronio s lectures on hyperbolic geometry if that whets your appetite.
Following some classical material on the hyperbolic space and the teichma. Princeton university press, 1997 lectures on hyperbolic geometry, r. We recommend iversen 1993 for starters, and benedetti and petronio 1992. Ebooks pdf lectures on hyperbolic geometry universitext. The arithmetic of hyperbolic 3manifolds by machlachlan and reid. Introduction to hyperbolic geometry 1 topics i geometry of real and complex hyperbolic space.
This notion is only not so commonly used in undergraduate textbooks nowadays, probably because, in many cases, the mathematical objects to be discussed can be easily formulated in other equivalent ways. Oclcs webjunction has pulled together information and resources to assist library staff as they consider how to handle. 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. Shiota finiteness of semialgebraic types of polynomial functions math. Particular attention will be paid to topics of interest to the students, and the course will be shaped by these interests. Ams proceedings of the american mathematical society. Instead, we will develop hyperbolic geometry in a way that emphasises the similarities and more interestingly.
Lectures on hyperbolic geometry edition 1 by riccardo. Hyperbolic manifolds and the compact twodimensional case. D program in mathematics cuny graduate center spring 2012. This chapter is devoted to the definition of a riemannian nmanifold. Bonahon, geometric structures on 3manifolds, handbook of geometric topology, elsevier 2002 3 w. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. A new foreword for notes on notes of thurston mathematics. Ratcli e, graduate texts in mathematics 149, springerverlag, 1994 david dumas. Petronio, lectures on hyperbolic geometry, springer 1992. Basic facts on hyperbolic geometry and its aplication g slovensky c asopis pre geometriu a grafiku, ro c nik 8 2011, c islo 15, s. The book concerns the geometry of manifolds and in particular hyperbolic manifolds. The gromov norm of the manifold is the gromov norm of the fundamental class.
The main goal is to describe thurstons geometrisation of threemanifolds, proved by perelman in 2002. Everything from geodesics to gaussbonnet, starting with a. By author riccardo benedetti, by author carlo petronio. The book concerns the geometry of manifolds and in particular. Lectures on hyperbolic geometry by benedetti and petronio, springerverlag, isbn 354055534 2. After collecting some material about the geometry of the hyperbolic space and the teichmuller space, it centers on the two fundamental results. Ams conformal geometry and dynamics of the american. Munkholm, simplices of maximal volume in hyperbolic space, gromovs norm, and gromovs. Petronio lectures on hyperbolic geometry universitext. Software for 3manifold topology and normal surface theory. Petronio, lectures on hyperbolic geometry, universitext, springer, berlin. 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. Diy hyperbolic geometry kathryn mann written for mathcamp 2015 abstract and guide to the reader. The anglesum of a triangle does not exceed two right angles, or 180.
This is a set of notes from a 5day doityourself or perhaps discoverityourself introduction to hyperbolic geometry. Sorry, we are unable to provide the full text but you may find it at the following locations. Numerous and frequentlyupdated resource results are available from this search. Hyperbolic geometry is a subset of a large class of geometries called noneuclidean geometries. This book provides a selfcontained introduction to the topology and geometry of surfaces and threemanifolds. Interactive visualization of hyperbolic geometry using the. 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. This book provides an exposition of some fundamental results.
Concerns the geometry of manifolds and in particular hyperbolic manifolds. Ratcli e, foundations of hyperbolic manifolds, second edition, springer 2006 peter scott, the geometries of 3manifolds. Chapter 15 hyperbolic geometry math 4520, spring 2015 so far we have talked mostly about the incidence structure of points, lines and circles. I can recommend lowdimensional geometry by francis bonahon and chapter 2 of thurstons threedimensional geometry and topology ed. On the other hand hyperbolic geometry describes spacetime more conveniently. Lectures on hyperbolic geometry, universitext, springer. Pdf an introduction to geometric topology semantic scholar. Students will be introduced to various topics and interesting examples. In mathematics, the gromov norm or simplicial volume of a compact oriented nmanifold is a norm on the homology with real coefficients given by minimizing the sum of the absolute values of the coefficients over all singular chains representing a cycle. Lectures on hyperbolic geometry riccardo benedetti. Lectures on hyperbolic geometry pdf free download epdf.
Thurston, threedimensional geometry and topology, volume i, edited by silvio levy, princeton mathematical series, 35 1997. Petronio, lectures on hyperbolic geometry, new york. Retrieve articles in conformal geometry and dynamics of the american mathematical society with msc 2000. Lectures on hyperbolic geometry riccardo benedetti springer. 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. Benedetti petronio also contains a very detailed account of the common beginning of the proof. You can nd a more formal introduction in the book of benedetti and petronio bp. The latter has a particularly comprehensive bibliography. Reliable information about the coronavirus covid19 is available from the world health organization current situation, international travel. The gromov norm of the manifold is the gromov norm of the fundamental class it is named after mikhail gromov, who with. Similarly to the matterfree case, these spacetimes have nice.
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