By Nigel Higson
This paintings attracts jointly rules from algebraic topology, sensible research and geometry. it's a instrument - a way of conveying info between those 3 topics - 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 fundamental principles of analytic K-homology and increase a few of its functions. It encompasses a specified creation to the mandatory sensible research, through an exploration of the connections among K-homology and operator idea, 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 publication should still lead the reader to a few crucial notions of up to date examine in geometric useful research.
Read or Download Analytic K-Homology (Oxford Mathematical Monographs) PDF
Best Algebraic Geometry books
An available textual content introducing algebraic geometries and algebraic teams at complicated undergraduate and early graduate point, this e-book develops the language of algebraic geometry from scratch and makes use of it to establish the idea of affine algebraic teams from first rules. construction at the historical past fabric from algebraic geometry and algebraic teams, the textual content presents an creation to extra complicated and specialized fabric.
The speculation of elliptic curves is exceptional through its lengthy historical past and through the variety of the equipment which were utilized in its research. This publication treats the mathematics procedure in its sleek formula, by utilizing simple algebraic quantity concept and algebraic geometry. Following a short dialogue of the required algebro-geometric effects, the booklet proceeds with an exposition of the geometry and the formal workforce of elliptic curves, elliptic curves over finite fields, the complicated numbers, neighborhood fields, and worldwide fields.
This seriously class-tested e-book is an exposition of the theoretical foundations of hyperbolic manifolds. it's a either a textbook and a reference. A easy wisdom of algebra and topology on the first 12 months graduate point of an American college is believed. the 1st half is anxious with hyperbolic geometry and discrete teams.
Additional info for Analytic K-Homology (Oxford Mathematical Monographs)