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Algebraic topology

Most popular at the top

  • The Geometry of Spherical Space Form Groupsby P.B. Gilkey

    World Scientific Publishing Company 1989; US$ 129.00

    In this volume, the geometry of spherical space form groups is studied using the eta invariant. The author reviews the analytical properties of the eta invariant of Atiyah-Patodi-Singer and describes how the eta invariant gives rise to torsion invariants in both K-theory and equivariant bordism. The eta invariant is used to compute the K-theory of... more...

  • Intersection Cohomologyby Armand Borel

    Springer 2009; US$ 49.99

    This book is a publication in Swiss Seminars, a subseries of Progress in Mathematics. It is an expanded version of the notes from a seminar on intersection cohomology theory, which met at the University of Bern, Switzerland, in the spring of 1983. This volume supplies an introduction to the piecewise linear and sheaf-theoretic versions of that theory... more...

  • Symmetric Bendsby Roger E. Miles

    World Scientific Publishing Company 1995; US$ 68.00

    A bend is a knot securely joining together two lengths of cord (or string or rope), thereby yielding a single longer length. There are many possible different bends, and a natural question that has probably occurred to many is: “Is there a ‘best’ bend and, if so, what is it?”Most of the well-known bends happen to be symmetric... more...

  • Hypoelliptic Laplacian and Bott–Chern Cohomologyby Jean-Michel Bismut

    Springer 2013; US$ 109.00

    The book provides the proof of a complex geometric version of a well-known result in algebraic geometry: the theorem of Riemann-Roch-Grothendieck for proper submersions. It gives an equality of cohomology classes in Bott-Chern cohomology, which is a refinement for complex manifolds of de Rham cohomology. When the manifolds are Kähler, our main... more...

  • Spectra and the Steenrod Algebraby H.R. Margolis

    Elsevier Science 2011; US$ 148.25

    Spectra and the Steenrod Algebra more...

  • Rational Homotopy Theory and Differential Formsby Phillip Griffiths; John Morgan

    Springer 2013; US$ 109.00

    This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham?s theorem on... more...

  • Advances in the Homotopy Analysis Methodby Shijun Liao

    World Scientific Publishing Company 2013; US$ 163.00

    Unlike other analytic techniques, the Homotopy Analysis Method (HAM) is independent of small/large physical parameters. Besides, it provides great freedom to choose equation type and solution expression of related linear high-order approximation equations. The HAM provides a simple way to guarantee the convergence of solution series. Such uniqueness... more...

  • Functorial Knot Theoryby David N. Yetter

    World Scientific Publishing Company 2001; US$ 142.00

    Almost since the advent of skein-theoretic invariants of knots and links (the Jones, HOMFLY, and Kauffman polynomials), the important role of categories of tangles in the connection between low-dimensional topology and quantum-group theory has been recognized. The rich categorical structures naturally arising from the considerations of cobordisms have... more...

  • Energy of Knots and Conformal Geometryby Jun O'Hara

    World Scientific Publishing Company 2003; US$ 135.00

    Energy of knots is a theory that was introduced to create a “canonical configuration” of a knot — a beautiful knot which represents its knot type. This book introduces several kinds of energies, and studies the problem of whether or not there is a “canonical configuration” of a knot in each knot type. It also considers... more...

  • A History of Algebraic and Differential Topology, 1900 - 1960by Jean Dieudonne

    Springer 2009; US$ 89.99

    Since the early part of the 20th century, topology has gradually spread to many other branches of mathematics, and this book demonstrates how the subject continues to play a central role in the field. Written by a world-renowned mathematician, this classic text traces the history of algebraic topology beginning with its creation in the early 1900s... more...