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Author : Randecker, Anja
Publisher : KIT Scientific Publishing
ISBN 13 : 3731504561
Total Pages : 164 pages
Book Rating : 4.7/5 (315 download)
Download or read book Geometry and topology of wild translation surfaces written by Randecker, Anja and published by KIT Scientific Publishing. This book was released on 2016-04-28 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Anja Randecker
Publisher :
ISBN 13 : 9781013283932
Total Pages : 158 pages
Book Rating : 4.2/5 (839 download)
Download or read book Geometry and Topology of Wild Translation Surfaces written by Anja Randecker and published by . This book was released on 2020-10-09 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: A translation surface is a two-dimensional manifold, equipped with a translation structure. It can be obtained by considering Euclidean polygons and identifying their edges via translations. The vertices of the polygons form singularities if the translation structure can not be extended to them. We study translation surfaces with wild singularities, regarding the topology (genus and space of ends), the geometry (behavior of the singularities), and how the topology and the geometry are related. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Author : Ken’ichi Ohshika
Publisher : Springer Nature
ISBN 13 : 3030559289
Total Pages : 724 pages
Book Rating : 4.0/5 (35 download)
Download or read book In the Tradition of Thurston written by Ken’ichi Ohshika and published by Springer Nature. This book was released on 2020-12-07 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of 16 surveys on Thurston's work and its later development. The authors are mathematicians who were strongly influenced by Thurston's publications and ideas. The subjects discussed include, among others, knot theory, the topology of 3-manifolds, circle packings, complex projective structures, hyperbolic geometry, Kleinian groups, foliations, mapping class groups, Teichmüller theory, anti-de Sitter geometry, and co-Minkowski geometry. The book is addressed to researchers and students who want to learn about Thurston’s wide-ranging mathematical ideas and their impact. At the same time, it is a tribute to Thurston, one of the greatest geometers of all time, whose work extended over many fields in mathematics and who had a unique way of perceiving forms and patterns, and of communicating and writing mathematics.
Author : Athanase Papadopoulos
Publisher : Springer Nature
ISBN 13 : 3030866955
Total Pages : 469 pages
Book Rating : 4.0/5 (38 download)
Download or read book Surveys in Geometry I written by Athanase Papadopoulos and published by Springer Nature. This book was released on 2022-02-18 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume consists of a set of surveys on geometry in the broad sense. The goal is to present a certain number of research topics in a non-technical and appealing manner. The topics surveyed include spherical geometry, the geometry of finite-dimensional normed spaces, metric geometry (Bishop—Gromov type inequalities in Gromov-hyperbolic spaces), convexity theory and inequalities involving volumes and mixed volumes of convex bodies, 4-dimensional topology, Teichmüller spaces and mapping class groups actions, translation surfaces and their dynamics, and complex higher-dimensional geometry. Several chapters are based on lectures given by their authors to middle-advanced level students and young researchers. The whole book is intended to be an introduction to current research trends in geometry.
Author : Sebastian Baader
Publisher :
ISBN 13 : 9783985475001
Total Pages : pages
Book Rating : 4.4/5 (75 download)
Download or read book Geometry and Topology of Surfaces written by Sebastian Baader and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : José Luis Cisneros-Molina
Publisher : Springer Nature
ISBN 13 : 3030780244
Total Pages : 581 pages
Book Rating : 4.0/5 (37 download)
Download or read book Handbook of Geometry and Topology of Singularities II written by José Luis Cisneros-Molina and published by Springer Nature. This book was released on 2021-11-01 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of the Handbook of the Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory and related topics. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
Author : Alexandru Scorpan
Publisher : American Mathematical Society
ISBN 13 : 1470468611
Total Pages : 614 pages
Book Rating : 4.4/5 (74 download)
Download or read book The Wild World of 4-Manifolds written by Alexandru Scorpan and published by American Mathematical Society. This book was released on 2022-01-26 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: What a wonderful book! I strongly recommend this book to anyone, especially graduate students, interested in getting a sense of 4-manifolds. —MAA Reviews The book gives an excellent overview of 4-manifolds, with many figures and historical notes. Graduate students, nonexperts, and experts alike will enjoy browsing through it. — Robion C. Kirby, University of California, Berkeley This book offers a panorama of the topology of simply connected smooth manifolds of dimension four. Dimension four is unlike any other dimension; it is large enough to have room for wild things to happen, but small enough so that there is no room to undo the wildness. For example, only manifolds of dimension four can exhibit infinitely many distinct smooth structures. Indeed, their topology remains the least understood today. To put things in context, the book starts with a survey of higher dimensions and of topological 4-manifolds. In the second part, the main invariant of a 4-manifold—the intersection form—and its interaction with the topology of the manifold are investigated. In the third part, as an important source of examples, complex surfaces are reviewed. In the final fourth part of the book, gauge theory is presented; this differential-geometric method has brought to light how unwieldy smooth 4-manifolds truly are, and while bringing new insights, has raised more questions than answers. The structure of the book is modular, organized into a main track of about two hundred pages, augmented by extensive notes at the end of each chapter, where many extra details, proofs and developments are presented. To help the reader, the text is peppered with over 250 illustrations and has an extensive index.
Author : A. T. Fomenko
Publisher : Springer
ISBN 13 :
Total Pages : 348 pages
Book Rating : 4.3/5 (91 download)
Download or read book Visual Geometry and Topology written by A. T. Fomenko and published by Springer. This book was released on 1994 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : José Luis Cisneros-Molina
Publisher : Springer Nature
ISBN 13 : 3030957608
Total Pages : 822 pages
Book Rating : 4.0/5 (39 download)
Download or read book Handbook of Geometry and Topology of Singularities III written by José Luis Cisneros-Molina and published by Springer Nature. This book was released on 2022-06-06 with total page 822 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I and II, such as, for instance, Zariski’s equisingularity, the interplay between isolated complex surface singularities and 3-manifold theory, stratified Morse theory, constructible sheaves, the topology of the non-critical levels of holomorphic functions, and intersection cohomology. Other chapters bring in new subjects, such as the Thom–Mather theory for maps, characteristic classes for singular varieties, mixed Hodge structures, residues in complex analytic varieties, nearby and vanishing cycles, and more. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
Author : Ernesto Lupercio
Publisher : American Mathematical Soc.
ISBN 13 : 0821894943
Total Pages : 226 pages
Book Rating : 4.8/5 (218 download)
Download or read book The Influence of Solomon Lefschetz in Geometry and Topology written by Ernesto Lupercio and published by American Mathematical Soc.. This book was released on 2014-08-05 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The influence of Solomon Lefschetz (1884-1972) in geometry and topology 40 years after his death has been very profound. Lefschetz's influence in Mexican mathematics has been even greater. In this volume, celebrating 50 years of mathematics at Cinvestav-México, many of the fields of geometry and topology are represented by some of the leaders of their respective fields. This volume opens with Michael Atiyah reminiscing about his encounters with Lefschetz and México. Topics covered in this volume include symplectic flexibility, Chern-Simons theory and the theory of classical theta functions, toric topology, the Beilinson conjecture for finite-dimensional associative algebras, partial monoids and Dold-Thom functors, the weak b-principle, orbit configuration spaces, equivariant extensions of differential forms for noncompact Lie groups, dynamical systems and categories, and the Nahm pole boundary condition.
Author : William P. Thurston
Publisher : Princeton University Press
ISBN 13 : 9780691083049
Total Pages : 340 pages
Book Rating : 4.0/5 (83 download)
Download or read book Three-dimensional Geometry and Topology written by William P. Thurston and published by Princeton University Press. This book was released on 1997 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every mathematician should be acquainted with the basic facts about the geometry of surfaces, of two-dimensional manifolds. The theory of three-dimensional manifolds is much more difficult and still only partly understood, although there is ample evidence that the theory of three-dimensional manifolds is one of the most beautiful in the whole of mathematics. This excellent introductory work makes this mathematical wonderland remained rather inaccessible to non-specialists. The author is both a leading researcher, with a formidable geometric intuition, and a gifted expositor. His vivid descriptions of what it might be like to live in this or that three-dimensional manifold bring the subject to life. Like Poincaré, he appeals to intuition, but his enthusiasm is infectious and should make many converts for this kind of mathematics. There are good pictures, plenty of exercises and problems, and the reader will find a selection of topics which are not found in the standard repertoire. This book contains a great deal of interesting mathematics.
Author : William P. Thurston
Publisher : Princeton University Press
ISBN 13 : 1400865328
Total Pages : 323 pages
Book Rating : 4.4/5 (8 download)
Download or read book Three-Dimensional Geometry and Topology, Volume 1 written by William P. Thurston and published by Princeton University Press. This book was released on 2014-10-31 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty. This book was the origin of a grand scheme developed by Thurston that is now coming to fruition. In the 1920s and 1930s the mathematics of two-dimensional spaces was formalized. It was Thurston's goal to do the same for three-dimensional spaces. To do this, he had to establish the strong connection of geometry to topology--the study of qualitative questions about geometrical structures. The author created a new set of concepts, and the expression "Thurston-type geometry" has become a commonplace. Three-Dimensional Geometry and Topology had its origins in the form of notes for a graduate course the author taught at Princeton University between 1978 and 1980. Thurston shared his notes, duplicating and sending them to whoever requested them. Eventually, the mailing list grew to more than one thousand names. The book is the culmination of two decades of research and has become the most important and influential text in the field. Its content also provided the methods needed to solve one of mathematics' oldest unsolved problems--the Poincaré Conjecture. In 2005 Thurston won the first AMS Book Prize, for Three-dimensional Geometry and Topology. The prize recognizes an outstanding research book that makes a seminal contribution to the research literature. Thurston received the Fields Medal, the mathematical equivalent of the Nobel Prize, in 1982 for the depth and originality of his contributions to mathematics. In 1979 he was awarded the Alan T. Waterman Award, which recognizes an outstanding young researcher in any field of science or engineering supported by the National Science Foundation.
Author : John W. Morgan
Publisher : Lecture Notes in Mathematics
ISBN 13 :
Total Pages : 244 pages
Book Rating : 4.3/5 (91 download)
Download or read book Differential Topology of Complex Surfaces written by John W. Morgan and published by Lecture Notes in Mathematics. This book was released on 1993-08-30 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the smooth classification of a certain class of algebraicsurfaces, namely regular elliptic surfaces of geometric genus one, i.e. elliptic surfaces with b1 = 0 and b2+ = 3. The authors give a complete classification of these surfaces up to diffeomorphism. They achieve this result by partially computing one of Donalson's polynomial invariants. The computation is carried out using techniques from algebraic geometry. In these computations both thebasic facts about the Donaldson invariants and the relationship of the moduli space of ASD connections with the moduli space of stable bundles are assumed known. Some familiarity with the basic facts of the theory of moduliof sheaves and bundles on a surface is also assumed. This work gives a good and fairly comprehensive indication of how the methods of algebraic geometry can be used to compute Donaldson invariants.
Author : Igor Nikolaev
Publisher : Springer
ISBN 13 : 9783642086984
Total Pages : 450 pages
Book Rating : 4.0/5 (869 download)
Download or read book Foliations on Surfaces written by Igor Nikolaev and published by Springer. This book was released on 2010-12-09 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive, encyclopedic approach to the subject of foliations, one of the major concepts of modern geometry and topology. It addresses graduate students and researchers and serves as a reference book for experts in the field.
Author : E. E. Moise
Publisher :
ISBN 13 : 9781461299073
Total Pages : 276 pages
Book Rating : 4.2/5 (99 download)
Download or read book Geometric Topology in Dimensions 2 And 3 written by E. E. Moise and published by . This book was released on 2014-01-15 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Norbert A'Campo
Publisher :
ISBN 13 : 9783030890339
Total Pages : 0 pages
Book Rating : 4.8/5 (93 download)
Download or read book Topological, Differential and Conformal Geometry of Surfaces written by Norbert A'Campo and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincaré Lemma, the Morse Lemma, the classification of compact connected oriented surfaces, Stokes' Theorem, fixed point theorems and rigidity theorems. There is also a novel presentation of planar hyperbolic geometry. Moving on to more advanced concepts, it covers topics such as Riemannian metrics, the isometric torsion-free connection on vector fields, the Ansatz of Koszul, the Gauss-Bonnet Theorem, and integrability. These concepts are then used for the study of Riemann surfaces. One of the focal points is the Uniformization Theorem for compact surfaces, an elementary proof of which is given via a property of the energy functional. Among numerous other results, there is also a proof of Chow's Theorem on compact holomorphic submanifolds in complex projective spaces. Based on lecture courses given by the author, the book will be accessible to undergraduates and graduates interested in the analytic theory of Riemann surfaces.
Author : Danny Calegari
Publisher : Clarendon Press
ISBN 13 : 0191524638
Total Pages : 384 pages
Book Rating : 4.1/5 (915 download)
Download or read book Foliations and the Geometry of 3-Manifolds written by Danny Calegari and published by Clarendon Press. This book was released on 2007-05-17 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in 1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
