This volume consists of introductory lectures on the topics in the new and rapidly developing area of toric homotopy theory, and its applications to the current research in configuration spaces and braids, as well as to more applicable mathematics s…
Historically, for metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research. The history breaks naturally into two periods - the classical (separable metric) and the modern (not-necessa…
These papers survey the developments in General Topology and the applications of it which have taken place since the mid 1980s. The book may be regarded as an update of some of the papers in the Handbook of Set-Theoretic Topology (eds. Kunen/Vaughan…
Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz,…
The French mathematician and engineer Gerard Desargues (1591-1661) was one of the founders of projective geometry. Desargues' theorem is named in the honour of this prolific writer of treatises on geometry and its application to the arts and archite…
The aim of this book is to present the fundamental concepts and properties of the geodesic flow of a closed Riemannian manifold. The topics covered are close to my research interests. An important goal here is to describe properties of the geodesic…
Let $X$ be a smooth elliptic fibration over a smooth base $B$. Under mild assumptions, the authors establish a Fourier-Mukai equivalence between the derived categories of two objects, each of which is an $\mathcal{O}{\times}$ gerbe over a genus one…
In the more than 100 years since the fundamental group was first introduced by Henri Poincare it has evolved to play an important role in different areas of mathematics. Originally conceived as part of algebraic topology, this essential concept and…
This book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the Jones polynom…
Knots and links are studied by mathematicians, and are also finding increasing application in chemistry and biology. Many naturally occurring questions are often simple to state, yet finding the answers may require ideas from the forefront of resear…
A phenomenon which appears in nature, or human behavior, can sometimes be explained by saying that a certain potential function is maximized, or minimized. For example, the Hamiltonian mechanics, soapy films, size of an atom, business management, et…
Professor Peter Hilton is one of the best known mathematicians of his generation. He has published almost 300 books and papers on various aspects of topology and algebra. The present volume is to celebrate the occasion of his sixtieth birthday. It b…
This book contains a set of axioms for differential geometry and develops their consequences up to a point where a more advanced book might reasonably begin. Analytical operations with co-ordinate systems are continually used in differential geometr…
This is an introduction to geometrical topics that are useful in applied mathematics and theoretical physics, including manifolds, metrics, connections, Lie groups, spinors and bundles, preparing readers for the study of modern treatments of mechani…
Memoires ddis Georges de Rham.
One of the main achievements of algebraic geometry over the last 20 years is the work of Mori and others extending minimal models and the Enriques-Kodaira classification to 3-folds. This book is an integrated suite of papers centred around applicati…
The theory of soliton equations and integrable systems has developed rapidly over the past 20 years with applications in both mechanics and physics. A flood of papers followed a work by Gardner, Green, Kruskal and Mizura about the Korteweg-de Vries…
This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory. The approach…
This book gives a quick introduction to the theory of foliations, Lie groupoids and Lie algebroids. An important feature is the emphasis on the interplay between these concepts: Lie groupoids form an indispensable tool to study the transverse struct…
Universal Spaces and Mappings is devoted to universality problems. A new approach to these problems is given using some specific spaces. Since the construction of these specific spaces is set-theoretical, the given theory can be applied to different…
'Ht moi *..., si favait su comment en reveniT, One service mathematics hal rendered the je n'y serais point aile.' human race. It has put C
This volume consists of the proceedings of a conference held at the University College of North Wales (Bangor) in July of 1979. It assembles research papers which reflect diverse currents in low-dimensional topology. The topology of 3-manifolds, hyp…
This introductory textbook for a graduate course in pure mathematics provides a gateway into the two difficult fields of algebraic geometry and commutative algebra. Algebraic geometry, supported fundamentally by commutative algebra, is a cornerstone…
This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology, and will also be of interest to researchers. This is the first textbook to include topics such as Mors…
Die Theorie der konvexen Mengen stellt insofern eine besonders reizvolle mathe- matische Disziplin dar, als es in ihrem Rahmen moglich ist, aus wenigen, anschau- lich unmittelbar einsichtigen Voraussetzungen geometrisch wie analytisch in glei- cher…
The first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to questions of solvability of algebraic equations in explicit form. The second part describes a surprising analogy betw…
Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety…
To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology…
This work confronts the question of geometric processes of derivation, specifically the derivation of affine planes - keying in on construction techniques and types of transformations in which lines of a newly-created plane can be understood as subp…
This proceedings volume centers on new developments in rational homotopy and on their influence on algebra and algebraic topology. Most of the papers are original research papers dealing with rational homotopy and tame homotopy, cyclic homology, Moo…
This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be ab…
A substantially revised edition of the UTM volume, with a view to making the book far more accessible to undergraduates. It contains a larger number of detailed explanations and exercises, together with fully worked solutions to the essential proble…
The main purpose of the present volume is to give a survey of some of the most significant achievements obtained by topological methods in nonlin ear analysis during the last three decades. It is intended, at least partly, as a continuation of Topol…
Celebrating a century of geometry and geometry teaching, this book will give the reader an enjoyable insight into all things geometrical. There are a wealth of popular articles including sections on Pythagoras, the golden ratio and recreational geom…
This book presents a compendium style account of a comprehensive mathematical journey from Arithmetic to Algebra. It contains material that is helpful to graduate and advanced undergraduate students in mathematics, university and college professors…
This book collects the scientific contributions of a group of leading experts who took part in the INdAM Meeting held in Cortona in September 2014. With combinatorial techniques as the central theme, it focuses on recent developments in configuratio…
Topics in Knot Theory is a state of the art volume which presents surveys of the field by the most famous knot theorists in the world. It also includes the most recent research work by graduate and postgraduate students. The new ideas presented cove…
In the long run of a dynamical system, after transient phenomena have passed away, what remains is recurrence. An orbit is recurrent when it returns repeatedly to each neighborhood of its initial position. We can sharpen the concept by insisting tha…
The Motivation. With intensified use of mathematical ideas, the methods and techniques of the various sciences and those for the solution of practical problems demand of the mathematician not only greater readi ness for extra-mathematical applicatio…
This book is based on the proceedings of the Fifth Northeast Conference on General Topology and Applications, held at The College of Staten Island - The City University of New York. It provides insight into the relationship between general topology…
Fixed-point algorithms have diverse applications in economics, optimization, game theory and the numerical solution of boundary-value problems. Since Scarf's pioneering work [56,57] on obtaining approximate fixed points of continuous mappings, a gre…
In 1992 two successive symposia were held in Japan on algorithms, fractals and dynamical systems. The first one was Hayashibara Forum '92: International Symposium on New Bases for Engineering Science, Algorithms, Dynamics and Fractals held at Fujisa…
This book discusses the equivariant cohomology theory of differentiable manifolds. Although this subject has gained great popularity since the early 1980's, it has not before been the subject of a monograph. It covers almost all important aspects of…
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 cosmo…
In this book, Claire Voisin provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. The volume is intended for both…
This is a genuine introduction to plane algebraic curves from a geometric viewpoint, designed as a first text for undergraduates in mathematics, or for postgraduate and research workers in the engineering and physical sciences. The book contains sev…