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Polytopes, Rings, and K-Theory (Hardcover, 2009 ed.)
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Polytopes, Rings, and K-Theory (Hardcover, 2009 ed.)
Series: Springer Monographs in Mathematics
Expected to ship within 12 - 17 working days
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For every mathematician, ring theory and K-theory are intimately
connected: al- braic K-theory is largely the K-theory of rings. At
?rst sight, polytopes, by their very nature, must appear alien to
surveyors of this heartland of algebra. But in the presence of a
discrete structure, polytopes de?ne a?ne monoids, and, in their
turn, a?ne monoids give rise to monoid algebras. Teir spectra are
the building blocks of toric varieties, an area that has developed
rapidly in the last four decades. From a purely systematic
viewpoint, "monoids" should therefore replace "po- topes" in the
title of the book. However, such a change would conceal the
geometric ?avor that we have tried to preserve through all
chapters. Before delving into a description of the contents we
would like to mention three general features of the book: (?) the
exhibiting of interactions of convex geometry, ring theory, and
K-theory is not the only goal; we present some of the central
results in each of these ?elds; (?) the exposition is of
constructive (i. e., algorithmic) nature at many places throughout
the text-there is no doubt that one of the driving forces behind
the current popularity of combinatorial geometry is the quest for
visualization and computation; (? ) despite the large amount of
information from various ?elds, we have strived to keep the
polytopal perspective as the major organizational principle.
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