Benedetti petronio lectures on hyperbolic geometry pdf

At this point the hyperboloid model is introduced, related to the other models visited, and developed using some concepts from physics as aids. Petronio, lectures on hyperbolic geometry, new york. Three are conformal models associated with the name of henri poincar e. Petronio, lectures on hyperbolic geometry, springer 1992. Euclidean geometry is usually the most convenient to describe the physical world surrounding us. Chapter 15 hyperbolic geometry math 4520, spring 2015 so far we have talked mostly about the incidence structure of points, lines and circles. Pdf basic facts on hyperbolic geometry and its applications. Ams conformal geometry and dynamics of the american.

Ratcli e, graduate texts in mathematics 149, springerverlag, 1994 david dumas. Petronio, lectures on hyperbolic geometry, universitext, springer, berlin. Calegari, foliations and the geometry of 3manifolds, oxford university press 2007. Petronio, universitext, springerverlag, 1991 foundations of hyperbolic manifolds, j. Lectures on the geometry of manifolds download pdfepub. This book provides a selfcontained introduction to the topology and geometry of surfaces and threemanifolds. We recommend iversen 1993 for starters, and benedetti and petronio 1992. A new foreword for notes on notes of thurston mathematics. Lectures on hyperbolic geometry pdf free download epdf. After collecting some material about the geometry of the hyperbolic space and the teichmuller space, it centers on the two fundamental results. The gromov norm of the manifold is the gromov norm of the fundamental class it is named after mikhail gromov, who with. Ratcli e, foundations of hyperbolic manifolds, second edition, springer 2006 peter scott, the geometries of 3manifolds. The anglesum of a triangle does not exceed two right angles, or 180.

Munkholm, simplices of maximal volume in hyperbolic space, gromovs norm, and gromovs. Benedetti petronio also contains a very detailed account of the common beginning of the proof. Three are conformal models associated with the name of henri poincar. Lectures on hyperbolic geometry by riccardo benedetti, 9783540555346, available at book.

This book provides an exposition of some fundamental results. The book concerns the geometry of manifolds and in particular hyperbolic manifolds. Shiota finiteness of semialgebraic types of polynomial functions math. Introduction to hyperbolic geometry 1 topics 2 bibliography. Mathematics 9 classical geometry and lowdimensional. Software for 3manifold topology and normal surface theory. Benedetti petronio lectures on hyperbolic geometry pdf. Instead, we will develop hyperbolic geometry in a way that emphasises the similarities and more interestingly. Petronio, lectures on hyperbolic geometry, universitext, springer verlag 1991 2 f.

Students will be introduced to various topics and interesting examples. Diy hyperbolic geometry kathryn mann written for mathcamp 2015 abstract and guide to the reader. Lectures on hyperbolic geometry by riccardo benedetti, 9783540555346, available at book depository with free delivery worldwide. Most importantly, benedettipetronio contains very complete proofs of the mostow rigidity theorem, marguliss lemma, thurstons hyperbolic dehn surgery. Petronio lectures on hyperbolic geometry universitext. Hyperbolic manifolds and the compact twodimensional case. Ams proceedings of the american mathematical society. Similarly to the matterfree case, these spacetimes have nice. Petronio universitext, springerverlag, 1991 invitation to geometry h. In this course we will study interactions between the geometry of the group, topology and algebra. Riccardo benedetti carlo petronio lectures on hyperbolic geometry with 175 figures springer. Everything from geodesics to gaussbonnet, starting with a. The gromov norm of the manifold is the gromov norm of the fundamental class. Volumes have been written on noneuclidean geometry, which the reader must consult for more exhaustive information.

Time and location description prerequisites organization. On the other hand hyperbolic geometry describes spacetime more conveniently. You could go on to al mardens outer circles or benedetti and petronio s lectures on hyperbolic geometry if that whets your appetite. Hyperbolic 3manifolds math 86500 17462 spring 2012. Lectures on hyperbolic geometry by riccardo benedetti,carlo petronio book resume. This is a set of notes from a 5day doityourself or perhaps discoverityourself introduction to hyperbolic geometry. Following some classical material on the hyperbolic space and the teichma. Ratcliffe graduate texts in mathematics 149, springerverlag, 1994. Reliable information about the coronavirus covid19 is available from the world health organization current situation, international travel.

The latter has a particularly comprehensive bibliography. Sorry, we are unable to provide the full text but you may find it at the following locations. Chapter 2 for hyperbolic plane and chapter 9 hyperbolic space from the book lowdimensional geometry by francis bonahon. Hyperbolic geometry 63 we shall consider in this exposition. Introduction to hyperbolic geometry 1 topics i geometry of real and complex hyperbolic space. 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 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. We also mentioned in the beginning of the course about euclids fifth postulate. Lectures on hyperbolic geometry riccardo benedetti. Lectures on hyperbolic geometry edition 1 by riccardo. Hyperbolic geometry 63 we shall consider in this exposition ve of the most famous of the analytic models of hyperbolic geometry.

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. Concerns the geometry of manifolds and in particular hyperbolic manifolds. In order to do that, some time is spent on neutral geometry as well as euclidean geometry. Page 2 mt5830 about this course hyperbolic geometry is a beautiful subject which blends ideas from algebra, analysis and geometry. 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. Interactive visualization of hyperbolic geometry using the. 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. 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.

Riccardo benedetti and carlo petronio, lectures on hyperbolic geometry, springer 2003 francis bonahon, lowdimensional geometry. Lectures on hyperbolic geometry, universitext, springer. Reviews benedetti petronio lectures on hyperbolic geometry pdf is best in online store. Lowdimensional geometry by francis bonahon, ams, isbn 9780821848166 3. Lectures on hyperbolic geometry edition 1 available in paperback. Princeton university press, 1997 lectures on hyperbolic geometry, r. Ratcli e, springerverlag gtm 149, isbn 038794348x 4.

Hyperbolic geometry in two and three dimensions abstract. Lectures on hyperbolic geometry riccardo benedetti springer. Lectures on hyperbolic geometry riccardo benedetti, carlo. Introduction to hyperbolic geometry 1 topics i geometry of real and complex hyperbolic space models of hyperbolic space. But geometry is concerned about the metric, the way things are measured. 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, 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. A conformal model is one for which the metric is a pointbypoint scaling of the euclidean metric. Retrieve articles in conformal geometry and dynamics of the american mathematical society with msc 2000. D program in mathematics cuny graduate center spring 2012.

You can nd a more formal introduction in the book of benedetti and petronio bp. Lectures on hyperbolic geometry by benedetti and petronio, springerverlag, isbn 354055534 2. Lectures on hyperbolic geometry riccardo benedetti, cario petronio download bok. 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.

Lectures on hyperbolic geometry riccardo benedetti, cario. Oclcs webjunction has pulled together information and resources to assist library staff as they consider how to handle. Ebooks pdf lectures on hyperbolic geometry universitext. Albert einsteins special theory of relativity is based on hyperbolic. 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. By author riccardo benedetti, by author carlo petronio. Hyperbolic geometry is a subset of a large class of geometries called noneuclidean geometries. 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. Thurston, threedimensional geometry and topology, volume i, edited by silvio levy, princeton mathematical series, 35 1997. The arithmetic of hyperbolic 3manifolds by machlachlan and reid. Numerous and frequentlyupdated resource results are available from this search. The main goal is to describe thurstons geometrisation of threemanifolds, proved by perelman in 2002.

Pdf an introduction to geometric topology semantic scholar. However, formatting rules can vary widely between applications and fields of interest or study. The book concerns the geometry of manifolds and in particular. Riccardo benedetti and carlo petronio, lectures on hyperbolic geometry, universitext, springerverlag, berlin, 1992. This chapter is devoted to the definition of a riemannian nmanifold. Bonahon, geometric structures on 3manifolds, handbook of geometric topology, elsevier 2002 3 w. Lectures on the geometry of manifolds download pdf. 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.