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Algebraic topology

  • Knotsby Gerhard Burde; Heiner Zieschang; Michael Heusener

    De Gruyter 2013; US$ 140.00

    This 3. edition is an introduction to classical knot theory. It contains many figures and some tables of invariants of knots. This comprehensive account is an indispensable reference source for anyone interested in both classical and modern knot theory. Most of the topics considered in the book are developed in detail; only the main properties of fundamental... 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...

  • 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...

  • The Elements of Cantor Setsby Robert W. Vallin

    Wiley 2013; US$ 89.95

    A systematic and integrated approach to Cantor Sets and their applications to various branches of mathematics The Elements of Cantor Sets: With Applications features a thorough introduction to Cantor Sets and applies these sets as a bridge between real analysis, probability, topology, and algebra. The author fills a gap in the current literature... 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...

  • Hyperbolic Problems: Theory, Numerics and Applications (Volume 2)by Song Jiang; Tatsien Li

    World Scientific Publishing Company 2012; US$ 244.00

    This two-volume book is devoted to mathematical theory, numerics and applications of hyperbolic problems. Hyperbolic problems have not only a long history but also extremely rich physical background. The development is highly stimulated by their applications to Physics, Biology, and Engineering Sciences; in particular, by the design of effective numerical... more...

  • VIRTUAL KNOTSby Vassily Olegovich Manturov; Denis Petrovich Ilyutko

    World Scientific Publishing Company 2012; US$ 218.00

    The book is the first systematic research completely devoted to a comprehensive study of virtual knots and classical knots as its integral part. The book is self-contained and contains up-to-date exposition of the key aspects of virtual (and classical) knot theory.Virtual knots were discovered by Louis Kauffman in 1996. When virtual knot theory arose,... more...

  • The Local Structure of Algebraic K-Theoryby Bjørn Ian Dundas; Thomas G. Goodwillie; Randy McCarthy

    Springer 2012; US$ 129.00

    Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation... more...

  • Algebraic Invariants of Linksby Jonathan Hillman

    World Scientific Publishing Company 2012; US$ 140.00

    This book serves as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors. It emphasizes the features of the multicomponent case not normally considered by knot-theorists, such as longitudes, the homological complexity of many-variable Laurent polynomial rings, the fact that links are not usually... more...