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Homology theory

  • 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...

  • 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...

  • Etale Cohomology Theoryby Lei Fu

    World Scientific Publishing Company 2011; US$ 211.00

    Etale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and l-adic cohomology. The prerequisites... more...

  • The Geometry of Moduli Spaces of Sheavesby Daniel Huybrechts; Manfred Lehn

    Cambridge University Press 2010; US$ 45.00

    This highly regarded book is finally back in print and now updated to reflect recent advances in the field. 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...

  • Suites de Sturm, indice de Maslov et périodicité de Bott (Progress in Mathematics) (French Edition)by Jean Barge; Jean Lannes

    Springer 2008; US$ 69.95

    La théorie classique des suites de Sturm fournit un algorithme pour déterminer le nombre de racines d?un polynôme à coefficients réels contenues dans un intervalle donné. L?objet principal de ce mémoire est de montrer qu?une généralisation adéquate de la théorie des suites de Sturm fournit entre autres choses: une notion d?indice de Maslov pour un... more...

  • From Quantum Cohomology to Integrable Systemsby Martin A. Guest

    Oxford University Press, UK 2008; US$ 94.99

    This text focuses on the extraordinary success of quantum cohomology and its connections with many existing areas of traditional mathematics and new areas such as mirror symmetry. Aimed at graduate students in mathematics as well as theoretical physicists, the text assumes basic familiarity with differential equations and cohomology. - ;Quantum cohomology... more...

  • Rigid Cohomologyby Bernard Le Stum

    Cambridge University Press 2007; US$ 110.00

    The first book to give a complete treatment of rigid cohomology, from the basics to the very latest developments. more...

  • The Heart of Cohomologyby Goro Kato

    Springer 2006; US$ 135.00

    Explains fundamental notions in cohomology for examples, functors, representable functors, Yoneda embedding, drived functors, spectral sequences, derived categories. This work gives applications to sheaf cohomology. It also provides cohomological aspects of D-modules and of the computation of zeta functions of the Weierstrass family. more...

  • Representation Theory and Higher Algebraic K-Theoryby Aderemi Kuku

    Taylor and Francis 2006; US$ 129.95

    Representation Theory and Higher Algebraic K-Theory is the first book to present higher algebraic K-theory of orders and group rings as well as characterize higher algebraic K-theory as Mackey functors that lead to equivariant higher algebraic K-theory and their relative generalizations. Thus, this book makes computations of higher K-theory of group... more...