Topology

This 1989 monograph deals with parametric minimal surfaces in Euclidean space. The author presents a broad survey which extends from the classical beginnings to the current situation whilst highlighting many of the subject's main features and...

D-module theory is essentially the algebraic study of systems of linear partial differential equations. This book, the first devoted specifically to holonomic D-modules, provides a unified treatment of both regular and irregular D-modules. The authors...

Focusing on the role that automorphisms and equivalence relations play in the algebraic theory of minimal sets provides an original treatment of some key aspects of abstract topological dynamics. Such an approach is presented in this lucid and...

Noncommutative localization is a powerful algebraic technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. Originally conceived by algebraists (notably P. M. Cohn), it is now an important tool not...

Hyperbolic geometry is a classical subject in pure mathematics which has exciting applications in theoretical physics. In this book leading experts introduce hyperbolic geometry and Maass waveforms and discuss applications in quantum chaos and cosmology...

Topological K-theory is a key tool in topology, differential geometry and index theory, yet this is the first contemporary introduction for graduate students new to the subject. No background in algebraic topology is assumed; the reader need only have...

This textbook, for an undergraduate course in modern algebraic geometry, recognizes that the typical undergraduate curriculum contains a great deal of analysis and, by contrast, little algebra. Because of this imbalance, it seems most natural to present...

Presents reissued articles from two classic sources on hyperbolic manifolds. Part I is an exposition of Chapters 8 and 9 of Thurston's pioneering Princeton Notes; there is a new introduction describing recent advances, with an up-to-date bibliography,...

With hundreds of worked examples, exercises and illustrations, this detailed exposition of the theory of Vassiliev knot invariants opens the field to students with little or no knowledge in this area. It also serves as a guide to more advanced material...

The field of geometric variational problems is fast-moving and influential. These problems interact with many other areas of mathematics and have strong relevance to the study of integrable systems, mathematical physics and PDEs. The workshop...

This book brings together a selection of the best lectures from many graduate workshops held at the Australian National Institute for Theoretical Physics in Adelaide. The lectures presented here describe subjects currently of great interest, generally at...

Arakelov theory is a new geometric approach to diophantine equations. It combines algebraic geometry in the sense of Grothendieck with refined analytic tools such as currents on complex manifolds and the spectrum of Laplace operators. It has been used by...

Robert J. Zimmer is best known in mathematics for the highly influential conjectures and program that bear his name. Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers brings together some of the most significant writings by Zimmer,...

This book contains an in-depth overview of the current state of the recently emerged and rapidly growing theory of Gnk groups, picture-valued invariants, and braids for arbitrary manifolds. Equivalence relations arising in low-dimensional topology and...

This first of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It studies metric spaces and general topology. It starts with the concept of the metric which is an abstraction of...

Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. The authors' main goal in this 2005 book is to emphasize connections between classical projective differential geometry and contemporary mathematics and...

This work provides a lucid and rigorous account of the foundations of modern algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties, but...

The biennial meetings at Sao Carlos have helped create a worldwide community of experts and young researchers working on singularity theory, with a special focus on applications to a wide variety of topics in both pure and applied mathematics. The tenth...

Vector bundles and their associated moduli spaces are of fundamental importance in algebraic geometry. In recent decades this subject has been greatly enhanced by its relationships with other areas of mathematics, including differential geometry,...

An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition ". . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies...

Edward Witten once said that Elliptic Cohomology was a piece of 21st Century Mathematics that happened to fall into the 20th Century. He also likened our understanding of it to what we know of the topography of an archipelago; the peaks are beautiful and...

The 400-year-old Kepler conjecture asserts that no packing of congruent balls in three dimensions can have a density exceeding the familiar pyramid-shaped cannonball arrangement. In this book, a new proof of the conjecture is presented that makes it...

Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics. In this book, the rich geometry of the...

This volume is based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds. This area has been one of intense research during the 1990s, with major breakthroughs that have illuminated the way a...

Written for graduate students, this book presents topics in 2-dimensional hyperbolic geometry. The authors begin with rigid motions in the plane which are used as motivation for a full development of hyperbolic geometry in the unit disk. The approach is...

The book offers a good introduction to topology through solved exercises. It is mainly intended for undergraduate students. Most exercises are given with detailed solutions.Book InformationISBN 9789814583817Author Mohammed Hichem MortadFormat...

The Stacks Project Expository Collection (SPEC) compiles expository articles in advanced algebraic geometry, intended to bring graduate students and researchers up to speed on recent developments in the geometry of algebraic spaces and algebraic stacks...

This is a self-contained and systematic account of affine differential geometry from a contemporary view, not only covering the classical theory, but also introducing more modern developments. In order both to cover as much as possible and to keep the...

A selection of topics which graduate students have found to be a successful introduction to the field, employing three distinct techniques: geometric topology manoeuvres, combinatorics, and algebraic topology. Each topic is developed until significant...

Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book...

Moduli theory is the study of how objects, typically in algebraic geometry but sometimes in other areas of mathematics, vary in families and is fundamental to an understanding of the objects themselves. First formalised in the 1960s, it represents a...

gentle introduction to the subject, leading the reader to understand the notion of what is important in topology with regard to geometry. Divided into three sections - The line and the plane, Metric spaces and Topological spaces -, the book eases the...

Algebraic geometry is a central subfield of mathematics in which the study of cycles is an important theme. Alexander Grothendieck taught that algebraic cycles should be considered from a motivic point of view and in recent years this topic has spurred a...

This book presents a development of invariant manifold theory for a spe cific canonical nonlinear wave system -the perturbed nonlinear Schrooinger equation. The main results fall into two parts. The first part is concerned with the persistence and...

In Dual Models, written in the same enthusiastic style as its predecessors Polyhedron Models and Spherical Models, Magnus J. Wenninger presents the complete set of uniform duals of uniform polyhedral, thus rounding out a significant body of knowledge...

This definitive synthesis of mathematician Gregory Margulis's research brings together leading experts to cover the breadth and diversity of disciplines Margulis's work touches upon. This edited collection highlights the foundations and evolution of...

This book is a course in general topology, intended for students in the first year of the second cycle (in other words, students in their third univer sity year). The course was taught during the first semester of the 1979-80 academic year (three hours...

There are many reasons for writing this first volume of strategic activities on fractals. The most pervasive is the compelling desire to provide students of mathematics with a set of accessible, hands-on experiences with fractals and their underlying...

"A very valuable book. In little over 200 pages, it presents a well-organized and surprisingly comprehensive treatment of most of the basic material in differential topology, as far as is accessible without the methods of algebraic topology....There...

One of the first books to be dedicated specifically to metric spaces Full of worked examples, to get complex ideas across more easilyBook InformationISBN 9781852339227Author Satish ShiraliFormat PaperbackPage Count 222Imprint Springer London LtdPublisher...