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#### Simplicial Homotopy Theory

Springer 2009; US$ 69.99With the development of Quillen's concept of a closed model category and, in particular, a simplicial model category, the simplicial methods have become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in various fields, including algebraic K-theory. This book deals with these ideas. more...

#### Syzygies and Homotopy Theory

Springer 2011; US$ 109.00The most important invariant of a topological space is its fundamental group. When this is trivial, the resulting homotopy theory is well researched and familiar. In the general case, however, homotopy theory over nontrivial fundamental groups is much more problematic and far less well understood. Syzygies and Homotopy Theory explores the problem of... more...

#### Two-Dimensional Homotopy and Combinatorial Group Theory

Cambridge University Press 1993; US$ 92.00This book considers the current state of knowledge in the geometric and algebraic aspects of two-dimensional homotopy theory. more...

#### String Topology and Cyclic Homology

Springer 2006; US$ 39.95Deals with string topology, Hochschild and cyclic homology. This book consists of an exposition of various approaches to string topology and the Chas-Sullivan loop product. It also gives a construction of an algebraic model for computing topological cyclic homology. It is suitable for both graduate students and established researchers. more...

#### Lectures on Homotopy Theory

Elsevier Science 1992; US$ 72.95The central idea of the lecture course which gave birth to this book was to define the homotopy groups of a space and then give all the machinery needed to prove in detail that the n th homotopy group of the sphere S n , for n greater than or equal to 1 is isomorphic to the group of the integers, that the lower homotopy groups of S n are... more...

#### Algebraic Models in Geometry

Oxford University Press, UK 2008; US$ 55.00A text aimed at both geometers needing the tools of rational homotopy theory to understand and discover new results concerning various geometric subjects, and topologists who require greater breadth of knowledge about geometric applications of the algebra of homotopy theory. - ;Rational homotopy is a very powerful tool for differential topology and... more...

#### Stable Homotopy Around the Arf-Kervaire Invariant

Springer 2009; US$ 129.00Describes important techniques of stable homotopy theory, applying them to the long-standing problem of the existence of framed manifolds with odd Arf-Kervaire invariant. This work opens with an account of the necessary algebraic topology background. more...

#### Higher Structures in Geometry and Physics

Springer 2010; US$ 179.00This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics-- such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics-- and in theoretical physics such as quantum field theory and string theory.... more...

#### Homotopy Theory of C*-Algebras

Springer 2010; US$ 59.95Homotopy theory and C* algebras are central topics in contemporary mathematics. This book introduces a modern homotopy theory for C*-algebras. One basic idea of the setup is to merge C*-algebras and spaces studied in algebraic topology into one category comprising C*-spaces. These objects are suitable fodder for standard homotopy theoretic moves, leading... more...