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Stable Homotopy and Generalised Homology

cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology. Adams's exposition of the first two;

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Foundations of Stable Homotopy Theory

suitable for those with only a first course in algebraic topology. Starting from stable homotopy groups and (co)homology theories, the authors;

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Homotopy Theory with Bornological Coarse Spaces

. It introduces the category of bornological coarse spaces and the notion of a coarse homology theory, and further constructs the universal;

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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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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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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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Algebraic Topology

geometric approach to the Hurewicz theorem relating homology and homotopy. The last chapter exploits the algebraic invariants introduced in the book;

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Lectures on Factorization Homology Categories and Topological Field Theories

This book provides an informal and geodesic introduction to factorization homology, focusing on providing intuition through simple examples;

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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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Introduction to Functions of a Complex Variable

This book includes information on elementary general topology, the Cauchy Integral Theorem and concepts of homology and homotopy in their;

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Introduction to Functions of a Complex Variable

This book includes information on elementary general topology, the Cauchy Integral Theorem and concepts of homology and homotopy in their;

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Introduction to Algebraic Topology

theorem is proven in the groupoid version. Following this, an excursion to cofibrations and homotopy pushouts yields an alternative formulation;

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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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From Categories to Homotopy Theory

bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to;

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C*-Algebra Extensions and K-Homology. (AM-95), Volume 95

compact metrizable space X form an abelian group Ext (X). Second, he shows that the correspondence X ? Ext (X) defines a homotopy invariant;

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Algebraic Topology - Homotopy and Homology

From the reviews: The author has attempted an ambitious and most commendable project. [...] The book contains much material that has not;

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

known as the Elliott program. This includes some stable uniqueness theorems and a revisiting of Bott maps via stable homotopy. Furthermore, $KK;

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Representation Theory and Beyond

algebras, and the higher Auslander-Reiten theory studied via homotopy theory.;

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

, and Poincare duality. Because these applications have required repeated modifications of the original formulation of etale homotopy theory;

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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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An Alpine Bouquet of Algebraic Topology

spectra, infinity-categories and Segal spaces, equivariant homotopy theory, algebraic $K$-theory and topological cyclic, periodic, or Hochschild;

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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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Topology and Geometry

, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: An interesting and original;

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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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Bordered Heegaard Floer Homology

of which (type $D$) is a module over the algebra and the other of which (type $A$) is an $mathcal A_infty$ module. Both are well-defined up to;

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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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Bousfield Classes and Ohkawa's Theorem

information. This book contains developments for the rest of the story and much more, including the chromatics homotopy theory, which the;

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