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Commutator Calculus and Groups of Homotopy Classes

A fundamental problem of algebraic topology is the classification of homotopy types and homotopy classes of maps. In this work the author;

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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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An Introduction to Homotopy Theory

, the classical theorems, the exact homotopy sequence, fibre-spaces, the Hopf invariant, and the Freudenthal suspension. The final chapters;

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Calculus of Fractions and Homotopy Theory

category of CW-complexes modulo homotopy, i.e. the category whose objects are spaces of the homotopy type of a CW-complex and whose morphisms are;

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Combinatorial Group Theory

concepts and a discussion of factor groups and subgroups. The topics of Nielsen transformations, free and amalgamated products, and commutator;

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The Equationally-Defined Commutator

This monograph introduces and explores the notions of a commutator equation and the equationally-defined commutator from the perspective;

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The Homotopy Category of Simply Connected 4-Manifolds

homotopy classes of maps algebraically and determining the law of composition for such maps. This problem is solved in the book by introducing new;

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London Mathematical Society Lecture Note Series

extension theory from the viewpoint of derived objects and proves that for groups of period four, two-dimensional homotopy types are parametrized by;

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Cubical Homotopy Theory

Graduate students and researchers alike will benefit from this treatment of classical and modern topics in homotopy theory of topological;

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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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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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Global Homotopy Theory

bordism. Global equivariant homotopy theory studies such uniform phenomena, i.e. universal symmetries encoded by simultaneous and compatible;

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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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Bousfield Classes and Ohkawa's Theorem

theorem: the Bousfield classes in the stable homotopy category SH form a set. An inspiring, extensive mathematical story can be narrated starting;

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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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Fibre Bundles

Basic properties, homotopy classification, and characteristic classes of fibre bundles have become an essential part of graduate;

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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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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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Topology

This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra;

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Potential Theory and Geometry on Lie Groups

This book provides a complete and reasonably self-contained account of a new classification of connected Lie groups into two classes. The;

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Rational Homotopy Theory Ii

growth and structure of the rational homotopy groups of finite dimensional CW complexes, and concludes with a number of open questions.This;

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Basic Algebraic Topology

homotopy, fibrations and cofibrations, category theory, cell complexes, and simplicial complexes. It then focuses on the fundamental group;

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Simplicial Homotopy Theory

, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues;

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Model Categories And Their Localizations

equivalences plus two other classes of maps, called cofibrations and fibrations. Quillen's axioms ensure that the homotopy category exists and that the;

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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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Higher Categories and Homotopical Algebra

strong emphasis on homotopical algebra provides clear insights into classical constructions such as calculus of fractions, homotopy limits and;

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Polyphase Commutator Machines

This book was first published in 1951 and was written by designers of polyphase commutator machines for students, and for engineers;

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