To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re- lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ- ential topology, etc.), we concentrate our attention on concrete prob- lems in low dimensions, introducing only as much algebraic machin- ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject...
To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re- lations of th...
From the ancient origins of algebraic geometry in the solutions of polynomial equations, through the triumphs of algebraic geometry during the last two centuries, intersection theory has played a central role. The aim of this book is to develop the foundations of this theory, and to indicate the range of classical and modern applications. Although a comprehensive history of this vast subject is not attempted, the author points out some of the striking early appearances of the ideas of intersection theory. A suggested prerequisite for the reading of this book is a first course in algebraic...
From the ancient origins of algebraic geometry in the solutions of polynomial equations, through the triumphs of algebraic geometry during the last tw...
This book develops the combinatorics of Young tableaux and shows them in action in the algebra of symmetric functions, representations of the symmetric and general linear groups, and the geometry of flag varieties. The first part of the book is a self-contained presentation of the basic combinatorics of Young tableaux, including the remarkable constructions of "bumping" and "sliding," and several interesting correspondences. In Part II the author uses these results to study representations with geometry on Grassmannians and flag manifolds, including their Schubert subvarieties, and the...
This book develops the combinatorics of Young tableaux and shows them in action in the algebra of symmetric functions, representations of the symmetri...
Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and Riemann-Roch translate into simple facts about polytopes, toric varieties provide a marvelous source of examples in algebraic geometry. In the other direction, general facts from algebraic geometry have implications for such polytopes, such as to the problem of the number of lattice points they...
Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space wit...
Introduces some of the main ideas of modern intersection theory, traces their origins in classical geometry and sketches a few typical applications. Suitable for graduate students in mathematics, this book describes the construction and computation of intersection products by means of the geometry of normal cones.
Introduces some of the main ideas of modern intersection theory, traces their origins in classical geometry and sketches a few typical applications. S...
In various contexts of topology, algebraic geometry, and algebra (e.g. group representations), one meets the following situation. One has two contravariant functors K and A from a certain category to the category of rings, and a natural transformation p: K--+A of contravariant functors. The Chern character being the central exam ple, we call the homomorphisms Px: K(X)--+ A(X) characters. Given f: X--+ Y, we denote the pull-back homomorphisms by and fA: A(Y)--+ A(X). As functors to abelian groups, K and A may also be covariant, with push-forward homomorphisms and fA: A( X)--+ A(Y). Usually...
In various contexts of topology, algebraic geometry, and algebra (e.g. group representations), one meets the following situation. One has two contrava...
How did Federal Express decide to locate at the Memphis Airport? Why is China also losing manufacturing jobs? Do artists really help turn around a struggling neighborhood? What should you do with a declining auto mall - save it or let it die and start over again? What's better - subsidizing an business or subsidizing the infrastructure such a business requires? These are the kinds of questions that cities and states deal with all the time in their economic development. Bill Fulton's new book, ROMANCING THE SMOKESTACK: HOW CITIES AND STATES PURSUE PROSPERITY, is a collection of economic...
How did Federal Express decide to locate at the Memphis Airport? Why is China also losing manufacturing jobs? Do artists really help turn around a str...
