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Homotopy theory

Most popular at the top

  • Simplicial Homotopy Theoryby Paul G. Goerss

    Springer 2009; US$ 69.99

    With 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 Theoryby F.E.A. Johnson

    Springer 2011; US$ 109.00

    The 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 Theoryby Cynthia Hog-Angeloni; Wolfgang Metzler; Allan J. Sieradski

    Cambridge University Press 1993; US$ 92.00

    This book considers the current state of knowledge in the geometric and algebraic aspects of two-dimensional homotopy theory. more...

  • String Topology and Cyclic Homologyby Ralph L. Cohen; Kathryn Hess; Alexander A. Voronov

    Springer 2006; US$ 39.95

    Deals 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 Theoryby R.A. Piccinini

    Elsevier Science 1992; US$ 72.95

    The 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 Geometryby Yves Félix; John Oprea; Daniel Tanré

    Oxford University Press, UK 2008; US$ 55.00

    A 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 Invariantby Victor P. Snaith

    Springer 2009; US$ 129.00

    Describes 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...

  • Shape and Shape Theoryby D. G. Kendall; D. Barden; T. K. Carne; H. Le

    Wiley 2009; US$ 292.00

    "This is a fascinating book mixing geometry, topology and probability theory..." ( London Mathematical Society Bulletin , Vol 32, 2000) "The potential value that his volume should have to researchers in many areas for years to come." ( Short Book Reviews , August 2000) "I would like to conclude this review by strongly recommending that geodists... more...

  • Higher Structures in Geometry and Physicsby Alberto S. Cattaneo; Ping Xu; Anthony Giaquinto

    Springer 2010; US$ 179.00

    This 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*-Algebrasby Paul Arne Ostvaer

    Springer 2010; US$ 59.95

    Homotopy 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...