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Foundations of Stable Homotopy Theory

The beginning graduate student in homotopy theory is confronted with a vast literature on spectra that is scattered across books, articles;

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Stable Homotopy and Generalised Homology

J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the well;

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Nilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128

Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on;

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Representation Theory and Beyond

theory, as well as symmetries in the representation theory over an abstract stable homotopy theory. The second part consists of six more;

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From the Basic Homotopy Lemma to the Classification of $C^*$-algebras

elementary introduction to the technical part of the theory is given via a basic homotopy lemma concerning a pair of almost commuting unitaries. The;

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Global Homotopy Theory

Equivariant homotopy theory started from geometrically motivated questions about symmetries of manifolds. Several important equivariant;

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The Geometric Hopf Invariant and Surgery Theory

Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional;

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The Geometric Hopf Invariant and Surgery Theory

Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional;

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Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem

The long-standing Kervaire invariant problem in homotopy theory arose from geometric and differential topology in the 1960s and was quickly;

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Model Categories

category and its homotopy category. The author develops the theory of model categories, giving a careful development of the main examples. One;

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Cohomology Operations and Applications in Homotopy Theory

the algebraic structure of the cohomology ring has been instrumental to important progress in general homotopy theory and in specific;

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Stable Stems

The author presents a detailed analysis of 2-complete stable homotopy groups, both in the classical context and in the motivic context;

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Syzygies and Homotopy Theory

The most important invariant of a topological space is its fundamental group. When this is trivial, the resulting homotopy theory is well;

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ZZ/2 - Homotopy Theory

with the basic concepts of algebraic topology (homotopy, stable homotopy, homology, K-theory, the Pontrjagin-Thom transfer construction;

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Etale Homotopy of Simplicial Schemes. (AM-104), Volume 104

This book presents a coherent account of the current status of etale homotopy theory, a topological theory introduced into abstract;

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Homotopy Theory

This volume contains the proceedings of the conference Homotopy Theory: Tools and Applications, in honor of Paul Goerss's 60th birthday;

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K-Theory

, it is possible to derive a substantial part of stable homotopy theory from K-theory. The purpose of this book is to provide advanced;

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Advances in Two-Dimensional Homotopy and Combinatorial Group Theory

This volume presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Building on the foundations laid a;

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Algebraic Methods In Unstable Homotopy Theory

The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which;

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Homotopy Theory with Bornological Coarse Spaces

graduate students and researchers who want to learn about the homotopy-theoretical aspects of large scale geometry via the theory of infinity;

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An Introduction to Homotopy Theory

Since the introduction of homotopy groups by Hurewicz in 1935, homotopy theory has occupied a prominent place in the development;

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Lectures on Field Theory and Topology

These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special;

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Algebraic Homotopy

This book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed;

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Cambridge Studies in Advanced Mathematics

This book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed;

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Commutator Calculus and Groups of Homotopy Classes

extends results of rational homotopy theory to a subring of the rationale. The methods of proof employ classical commutator calculus of nilpotent;

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Homotopy of Operads and Grothendieck-Teichmuller Groups: Part 2

of developing a rational homotopy theory for operads. The book starts with a comprehensive review of the general theory of model categories and;

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The Homotopy Theory of ( ,1)-Categories

The notion of an ( ,1)-category has become widely used in homotopy theory, category theory, and in a number of applications. There are many;

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