Topology

Many of the developments of modern algebraic geometry and topology stem from the ideas of S.

This book is a Weekend Pocketbook on Everything You Should Know About the Shape of the Universe, the story of one of cosmology's oldest and biggest questions: what does the whole cosmos look like?

One of the great achievements of contemporary mathematics is the new understanding of four dimensions.

In the spring of 1985, A.

In this book, which may be used as a self-contained text for a beginning course, Professor Lefschetz aims to give the reader a concrete working knowledge of the central concepts of modern combinatorial topology: complexes, homology groups, mappings in spheres, homotopy, transformations and their fixed points, manifolds and duality theorems.

Topological analysis consists of those basic theorems of analysis which are essentially topological in character, developed and proved entirely by topological and pseudotopological methods.

This book presents many of the main developments of the past two decades in the study of real submanifolds in complex space, providing crucial background material for researchers and advanced graduate students.

During the summer of 1965, an informal seminar in geometric topology was held at the University of Wisconsin under the direction of Professor Bing.

A classic treatment of convergence and uniformity in topology from the acclaimed Annals of Mathematics Studies seriesPrinceton University Press is proud to have published the Annals of Mathematics Studies since 1940.

A classic treatment of topological methods in the theory of functions of a complex variable from the acclaimed Annals of Mathematics Studies seriesPrinceton University Press is proud to have published the Annals of Mathematics Studies since 1940.

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, Hopkins, and Smith in 1985.

A classic treatment of metric methods of Finsler spaces from the acclaimed Annals of Mathematics Studies seriesPrinceton University Press is proud to have published the Annals of Mathematics Studies since 1940.

This book describes an invariant, l, of oriented rational homology 3-spheres which is a generalization of work of Andrew Casson in the integer homology sphere case.

This book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial.

This collection brings together influential papers by mathematicians exploring the research frontiers of topology, one of the most important developments of modern mathematics.

The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology.

A classic treatment of elementary differential topology from the acclaimed Annals of Mathematics Studies seriesPrinceton University Press is proud to have published the Annals of Mathematics Studies since 1940.

Since Poincare's time, topologists have been most concerned with three species of manifold.

This book presents a coherent account of the current status of etale homotopy theory, a topological theory introduced into abstract algebraic geometry by M.

There is a sympathy of ideas among the fields of knot theory, infinite discrete group theory, and the topology of 3-manifolds.

The intention of the authors is to examine the relationship between piecewise linear structure and differential structure: a relationship, they assert, that can be understood as a homotopy obstruction theory, and, hence, can be studied by using the traditional techniques of algebraic topology.

A classic treatment of cohomology operations from the acclaimed Annals of Mathematics Studies seriesPrinceton University Press is proud to have published the Annals of Mathematics Studies since 1940.

One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years.

The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory.

Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics--such as in gauge theory.

On Knots is a journey through the theory of knots, starting from the simplest combinatorial ideas--ideas arising from the representation of weaving patterns.

A classic treatment of the Atiyah-Singer index theorem from the acclaimed Annals of Mathematics Studies seriesPrinceton University Press is proud to have published the Annals of Mathematics Studies since 1940.

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.

Measured geodesic laminations are a natural generalization of simple closed curves in surfaces, and they play a decisive role in various developments in two-and three-dimensional topology, geometry, and dynamical systems.

The need for an axiomatic treatment of homology and cohomology theory has long been felt by topologists.

Originally published as Volume 27 of the Princeton Mathematical series.

Written by Arthur Ogus on the basis of notes from Pierre Berthelot's seminar on crystalline cohomology at Princeton University in the spring of 1974, this book constitutes an informal introduction to a significant branch of algebraic geometry.

This book presents a new result in 3-dimensional topology.

The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds.

This book studies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over Q.

Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible.

Outer billiards is a basic dynamical system defined relative to a convex shape in the plane.

Though the search for good selectors dates back to the early twentieth century, selectors play an increasingly important role in current research.

This book is the first to present a new area of mathematical research that combines topology, geometry, and logic.

This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology.

This book presents the complete proof of the Bloch-Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry.

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.

By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical foundation for several exciting recent developments.

An inviting, intuitive, and visual exploration of differential geometry and formsVisual Differential Geometry and Forms fulfills two principal goals.

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.

John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P.

This book gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology.

William Thurston (1946-2012) was one of the great mathematicians of the twentieth century.

Surgery theory, the basis for the classification theory of manifolds, is now about forty years old.

The theme of this book is to establish a link between gauge theory and L²-cohomology theory.