Algebraic topology

Bridge the gap between category theory and its applications in homotopy theory with this guide for graduate students and researchers.

We dedicate this book to the memory of J.

Like the first Abel Symposium, held in 2004, the Abel Symposium 2015 focused on operator algebras.

Central to this collection of papers are new developments in the general theory of localization of spaces.

This book offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume.

The 20 years since the publication of this book have been an era of continuing growth and development in the field of algebraic topology.

This easy-to-cite handbook gives the first systematic treatment of the (co)end calculus in category theory and its applications.

Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory.

The D(2) problem is a fundamental problem in low dimensional topology.

This IMA Volume in Mathematics and its Applications TOWARDS HIGHER CATEGORIES contains expository and research papers based on a highly successful IMA Summer Program on n-Categories: Foundations and Applications.

Were I to take an iron gun, And ?

This monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of coherent sheaves of a compact complex manifold with values in its Bott-Chern cohomology, and the proof of a corresponding Riemann-Roch-Grothendieck  theorem.

Five years ago, I taught a one-quarter course in homological algebra.

In a detailed and comprehensive introduction to the theory of plane algebraic curves, the authors examine this classical area of mathematics that both figured prominently in ancient Greek studies and remains a source of inspiration and a topic of research to this day.

As the interaction of mathematics and theoretical physics continues to intensify, the theories developed in mathematics are being applied to physics, and conversely.

The guiding principle in this book is to use differential forms as an aid in exploring some of the less digestible aspects of algebraic topology.

This book is intended as a reference for mathematicians working with homological dimensions in commutative algebra and as an introduction to Gorenstein dimensions for graduate students with an interest in the same.

This selection of papers from the Beijing conference gives a cross-section of the current trends in the field of fixed point theory as seen by topologists and analysts.

This book serves as a textbook in real analysis.

This ambitious and original book sets out to introduce to mathematicians (even including graduate students ) the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in use.

The conjugate operator method is a powerful recently developed technique for studying spectral properties of self-adjoint operators.

This book is the fifth and final volume of Raoul Bott's Collected Papers.

The first systematic account of the basic theory of normed algebras, without assuming associativity.

Intersection cohomology assigns groups which satisfy a generalized form of Poincare duality over the rationals to a stratified singular space.

The aim of this book is to give as detailed a description as is possible of one of the most beautiful and complicated examples in low-dimensional topology.

The Farrell-Jones isomorphism conjecture in algebraic K-theory offers a description of the algebraic K-theory of a group using a generalized homology theory.

This monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary.

This volume is the Proceedings of the Third Korea-China-Japan Inter- national Symposium on Ring Theory held jointly with the Second Korea- Japan Joint Ring Theory Seminar which took place at the historical resort area of Korea, Kyongju, June 28-July 3, 1999.

This introductory volume provides the basics of surface-knots and related topics, not only for researchers in these areas but also for graduate students and researchers who are not familiar with the field.

This proceedings is a collection of articles on Topology and Teichmuller Spaces.

Since the subject of Groups of Self-Equivalences was first discussed in 1958 in a paper of Barcuss and Barratt, a good deal of progress has been achieved.

Freeness of an action of a compact Lie group on a compact Hausdorff space is equivalent to a simple condition on the corresponding equivariant K-theory.

Recent research has repeatedly led to connections between important rigidity questions and bounded cohomology.

The book introduces conceptually simple geometric ideas based on the existence of fundamental domains for metric G- spaces.

This text deals with A1-homotopy theory over a base field, i.

The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure written for students.

The book is based on my lecture notes "e;Infinite dimensional Morse theory and its applications"e;, 1985, Montreal, and one semester of graduate lectures delivered at the University of Wisconsin, Madison, 1987.

Represents the state of the art in the new field of synthetic differential topology.

The papers collected in this volume are contributions to the 43rd session of the Seminaire ' de mathematiques ' superieures ' (SMS) on "e;Morse Theoretic Methods in Nonlinear Analysis and Symplectic Topology.