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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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Foundations of Stable Homotopy Theory

and decades. There is much folklore but very few easy entry points. This comprehensive introduction to stable homotopy theory changes that. It;

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Algebraic Homotopy

, including an introduction to rational homotopy theory in terms of both differential Lie algebras and De Rham algebras. The author describes powerful;

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Cambridge Studies in Advanced Mathematics

, including an introduction to rational homotopy theory in terms of both differential Lie algebras and De Rham algebras. The author describes powerful;

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Cubical Homotopy Theory

pullbacks and pushouts, and the Blakers-Massey Theorem. Part II includes a brief example-driven introduction to categories, limits and colimits, an;

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An Illustrated Introduction to Topology and Homotopy

An Illustrated Introduction to Topology and Homotopy explores the beauty of topology and homotopy theory in a direct and engaging manner;

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Modal Homotopy Type Theory

pedigree. Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy offers an introduction to this new language and its modal;

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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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Algebraic L-theory and Topological Manifolds

. The algebraic L-theory assembly map is used to give a purely algebraic formulation of the Novikov conjectures on the homotopy invariance;

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Algebraic L-theory and Topological Manifolds

. The algebraic L-theory assembly map is used to give a purely algebraic formulation of the Novikov conjectures on the homotopy invariance;

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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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Motivic Homotopy Theory and Refined Enumerative Geometry

, at the Universitat Duisburg-Essen, Essen, Germany. It constitutes an accessible yet swift introduction to a new and active area within;

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London Mathematical Society Lecture Note Series

definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory;

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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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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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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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Higher Categories and Homotopical Algebra

This book provides an introduction to modern homotopy theory through the lens of higher categories after Joyal and Lurie, giving access to;

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London Mathematical Society Lecture Note Series

representation theory, plus an introduction to the etale homotopy theory of Artin and Mazur. Part two of the book features a milestone paper on the etale;

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ZZ/2 - Homotopy Theory

approach is elementary enough to provide an introduction to the subject suitable for graduate students although research workers will find here;

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Homotopy Theory

spectra associated to perfectoid fields, and the theory of higher homotopy operations.;

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Algebraic Methods In Unstable Homotopy Theory

, following a first course in homotopy theory. It is also a valuable reference for both experts and graduate students wishing to enter the field.;

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

. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date;

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Simplicial Homotopy Theory

to a homology theory, cosimplicial spaces, and homotopy coherence. Interspersed throughout are many results and ideas well-known to experts;

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Homotopy of Operads and Grothendieck-Teichmuller Groups: Part 2

The ultimate goal of this book is to explain that the Grothendieck-Teichmuller group, as defined by Drinfeld in quantum group theory, has a;

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Introduction to Functions of a Complex Variable

application to the Cauchy theory. It is intended for an introductory course in complex analysis at the first-year graduate and advanced undergraduate;

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Introduction to Functions of a Complex Variable

application to the Cauchy theory. It is intended for an introductory course in complex analysis at the first-year graduate and advanced undergraduate;

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