Topology

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.In the second edition, some significant changes have been made, other than the...

The book is an introduction to the foundations of Mathematics. The use of the constructive method in Arithmetic and the axiomatic method in Geometry gives a unitary understanding of the backgrounds of geometry, of its development and of its organic link...

This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. The first chapter discusses the meaning of surface and space and gives the classification of orientable surfaces. In...

This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. The first chapter discusses the meaning of surface and space and gives the classification of orientable surfaces. In...

This volume presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Building on the foundations laid a quarter of a century ago in the volume Two-dimensional Homotopy and Combinatorial Group Theory (LMS 197), the...

Algebraic varieties are shapes defined by polynomial equations. Smooth Fano threefolds are a fundamental subclass that can be thought of as higher-dimensional generalizations of ordinary spheres. They belong to 105 irreducible deformation families. This...

This book serves as a textbook for an introductory course in metric spaces for undergraduate or graduate students. The goal is to present the basics of metric spaces in a natural and intuitive way and encourage students to think geometrically while...

This book gives a brief treatment of the equivariant cohomology of the classical configuration space F( ^d,n) from its beginnings to recent developments. This subject has been studied intensively, starting with the classical papers of Artin (1925/1947)...

Solomon Lefschetz pioneered the field of topology--the study of the properties of many?sided figures and their ability to deform, twist, and stretch without changing their shape. According to Lefschetz, "If it's just turning the crank, it's algebra,...

This book introduces the theory of enveloping semigroups—an important tool in the field of topological dynamics—introduced by Robert Ellis. The book deals with the basic theory of topological dynamics and touches on the advanced concepts of the dynamics...

Traditionally, knot theory deals with diagrams of knots and the search of invariants of diagrams which are invariant under the well known Reidemeister moves. This book goes one step beyond: it gives a method to construct invariants for one parameter...

Group actions are an efficient way of describing symmetries in objects by defining the essential elements of a given object as a set. The symmetries of the object are then defined as the symmetry group of this set. "Groups of Circle...

From Backlund to Darboux, this monograph presents a comprehensive journey through the transformation theory of constrained Willmore surfaces, a topic of great importance in modern differential geometry and, in particular, in the field of integrable...

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, etc. In...

The 2019 'Australian-German Workshop on Differential Geometry in the Large' represented an extraordinary cross section of topics across differential geometry, geometric analysis and differential topology. The two-week programme featured talks from...

Written in celebration of Miles Reid's 70th birthday, this illuminating volume contains 11 papers by leading mathematicians in and around algebraic geometry, broadly related to the themes and interests of Reid's varied career. Just as in Reid's own...

This third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern...

Four-Dimensional Manifolds and Projective Structure may be considered first as an introduction to differential geometry and, in particular, to 4−dimensional manifolds, and secondly as an introduction to the study of projective structure and projective...

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...

K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi-Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent...

In this book Professor Kempf gives an introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint. By taking this view he is able to give a clean and lucid account of the subject which will be easily accessible to all...

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...

The principles of symmetry and self-similarity structure nature's most beautiful creations. For example, they are expressed in fractals, famous for their beautiful but complicated geometric structure, which is the subject of study in dimension theory...

This volume presents lecture notes based on the author's courses on Lie algebras and the solution of Hilbert's fifth problem. In chapter 1, "Lie Algebras," the structure theory of semi-simple Lie algebras in characteristic zero is presented,...

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 book provides an introduction to Riemannian geometry, the geometry of curved spaces, for use in a graduate course. Requiring only an understanding of differentiable manifolds, the author covers the introductory ideas of Riemannian geometry followed...

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...

Most integrable systems owe their origin to problems in geometry and they are best understood in a geometrical context. This is especially true today when the heroic days of KdV-type integrability are over. Problems that can be solved using the inverse...

The book is the first systematic research completely devoted to a comprehensive study of virtual knots and classical knots as its integral part. The book is self-contained and contains up-to-date exposition of the key aspects of virtual (and classical)...

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,...

An advanced treatment of surgery theory for graduate students and researchersSurgery theory, a subfield of geometric topology, is the study of the classifications of manifolds. A Course on Surgery Theory offers a modern look at this important...

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...

This graduate textbook offers a self-contained introduction to the concepts and techniques of logarithmic geometry, a key tool for analyzing compactification and degeneration in algebraic geometry and number theory. It features a systematic exposition of...

Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The underlying mathematics, known as the theory of aperiodic order, is the subject of this comprehensive multi-volume series...

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...