By Nigel Higson

This paintings attracts jointly principles from algebraic topology, useful research and geometry. it's a device - a method of conveying details between those 3 matters - and it's been used with good fortune to find theorems throughout a large span of arithmetic. the aim of this e-book is to acquaint the reader with the basic principles of analytic K-homology and boost a few of its functions. It encompasses a particular advent to the mandatory useful research, by means of an exploration of the connections among K-homology and operator concept, coarse geometry, index idea, and meeting maps, together with a close therapy of the Atiyah-Singer Index Theorem. starting with the rudiments of C* - algebra thought, the booklet may still lead the reader to a few critical notions of up to date study in geometric useful research.

**Read or Download Analytic K-Homology (Oxford Mathematical Monographs) PDF**

**Similar Algebraic Geometry books**

**The Many Facets of Geometry: A Tribute to Nigel Hitchin (Oxford Science Publications)**

Few humans have proved extra influential within the box of differential and algebraic geometry, and in exhibiting how this hyperlinks with mathematical physics, than Nigel Hitchin. Oxford University's Savilian Professor of Geometry has made primary contributions in components as varied as: spin geometry, instanton and monopole equations, twistor concept, symplectic geometry of moduli areas, integrables structures, Higgs bundles, Einstein metrics, hyperkähler geometry, Frobenius manifolds, Painlevé equations, detailed Lagrangian geometry and replicate symmetry, conception of grebes, and plenty of extra.

First textbook-level account of simple examples and strategies during this sector. appropriate for self-study via a reader who is familiar with a bit commutative algebra and algebraic geometry already. David Eisenbud is a well known mathematician and present president of the yank Mathematical Society, in addition to a profitable Springer writer.

**Measure, Topology, and Fractal Geometry (Undergraduate Texts in Mathematics)**

According to a direction given to gifted high-school scholars at Ohio collage in 1988, this publication is basically a complicated undergraduate textbook in regards to the arithmetic of fractal geometry. It well bridges the distance among conventional books on topology/analysis and extra really expert treatises on fractal geometry.

**Higher-Dimensional Algebraic Geometry (Universitext)**

The class thought of algebraic forms is the point of interest of this booklet. This very energetic sector of study continues to be constructing, yet an grand volume of information has collected over the last two decades. The authors aim is to supply an simply obtainable creation to the topic. The ebook starts off with preparatory and conventional definitions and effects, then strikes directly to talk about quite a few facets of the geometry of soft projective forms with many rational curves, and finishes in taking the 1st steps in the direction of Moris minimum version application of class of algebraic forms by way of proving the cone and contraction theorems.

**Extra resources for Analytic K-Homology (Oxford Mathematical Monographs)**