Topics in Algebraic and Analytic Geometry. (MN-13): Notes by Phillip A. Griffiths, John Frank Adams

By Phillip A. Griffiths, John Frank Adams

This quantity bargains a scientific remedy of convinced uncomplicated elements of algebraic geometry, offered from the analytic and algebraic issues of view. The notes specialise in comparability theorems among the algebraic, analytic, and non-stop categories.

Contents comprise: 1.1 sheaf conception, ringed areas; 1.2 neighborhood constitution of analytic and algebraic units; 1.3 P
n 2.1 sheaves of modules; 2.2 vector bundles; 2.3 sheaf cohomology and computations on P
n; 3.1 greatest precept and Schwarz lemma on analytic areas; 3.2 Siegel's theorem; 3.3 Chow's theorem; 4.1 GAGA; 5.1 line bundles, divisors, and maps to P
n; 5.2 Grassmanians and vector bundles; 5.3 Chern sessions and curvature; 5.4 analytic cocycles; 6.1 K-theory and Bott periodicity; 6.2 K-theory as a generalized cohomology concept; 7.1 the Chern personality and obstruction concept; 7.2 the Atiyah-Hirzebruch spectral series; 7.3 K-theory on algebraic forms; 8.1 Stein manifold idea; 8.2 holomorphic vector bundles on polydisks; 9.1 concluding feedback; bibliography.

Originally released in 1974.

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Complex Topological K-Theory by Efton Park

By Efton Park

Topological K-theory is a key device in topology, differential geometry and index conception, but this can be the 1st modern creation for graduate scholars new to the topic. No heritage in algebraic topology is believed; the reader desire in simple terms have taken the traditional first classes in actual research, summary algebra, and point-set topology. The e-book starts with a close dialogue of vector bundles and similar algebraic notions, via the definition of K-theory and proofs of an important theorems within the topic, equivalent to the Bott periodicity theorem and the Thom isomorphism theorem. The multiplicative constitution of K-theory and the Adams operations also are mentioned and the ultimate bankruptcy info the development and computation of attribute periods. With each vital element of the subject lined, and workouts on the finish of every bankruptcy, this is often the definitive booklet for a primary direction in topological K-theory.

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Monoidal Topology: A Categorical Approach to Order, Metric, by Dirk Hofmann, Gavin J. Seal, Walter Tholen

By Dirk Hofmann, Gavin J. Seal, Walter Tholen

Monoidal Topology describes an lively examine quarter that, after quite a few earlier proposals on tips to axiomatize 'spaces' by way of convergence, started to emerge before everything of the millennium. It combines Barr's relational presentation of topological areas by way of ultrafilter convergence with Lawvere's interpretation of metric areas as small different types enriched over the prolonged genuine half-line. for this reason, built with a quantale V (replacing the reals) and a monad T (replacing the ultrafilter monad) laxly prolonged from set maps to V-valued kinfolk, the ebook develops a specific conception of (T,V)-algebras that's encouraged concurrently by means of its metric and topological roots. The e-book highlights specifically the celebrated function of equationally outlined buildings in the given lax-algebraic context and provides a variety of new effects starting from topology and process conception to area concept. the entire precious pre-requisites so as and class idea are awarded within the booklet.

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