Topology

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...

What is the best way to divide a 'cake' and allocate the pieces among some finite collection of players? In this book, the cake is a measure space, and each player uses a countably additive, non-atomic probability measure to evaluate the size of the...

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...

Praise for George Francis's A Topological Picturebook: Bravo to Springer for reissuing this unique and beautiful book! It not only reminds the older generation of the pleasures of doing mathematics by hand, but also shows the new generation what ``hands...

After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. These books explore various new notions of space, including both formal and conceptual points...

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...

In this monograph the authors present detailed and pedagogic proofs of persistence theorems for normally hyperbolic invariant manifolds and their stable and unstable manifolds for classes of perturbations of the NLS equation, as well as for the existence...

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...

The Assouad dimension is a notion of dimension in fractal geometry that has been the subject of much interest in recent years. This book, written by a world expert on the topic, is the first thorough account of the Assouad dimension and its many variants...

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 a...

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...

Topological analysis consists of those basic theorems of analysis which are essentially topological in character, developed and proved entirely by topological and pseudotopological methods. The objective of this volume is the promotion, encouragement,...

This second of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, algebra, and the theory of...

After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. This book and its companion explore various new notions of space, including both formal and...

These notes arise from lectures presented in Florence under the auspices of the Accadamia dei Lincee and deal with an area that lies at the crossroads of mathematics and physics. The material presented here rests primarily on the pioneering work of...

The book contains a large number of examples and exercises. One chapter is fully devoted to the construction of the fundamental groups of some surfaces and topological spaces. Borsuk's theory of retracts is fully developed in one chapter, too. Five...

This book explores toric topology, polyhedral products and related mathematics from a wide range of perspectives, collectively giving an overview of the potential of the areas while contributing original research to drive the subject forward in...