Author: Simon Donaldson
Publisher:
Published: 2017-09-30
Total Pages: 694
ISBN-13: 9781571463395
DOWNLOAD EBOOK →These papers have been organized into five volumes by subject matter. The first volume deals with topology, the second with algebraic geometry, the third with geometric ideas, the fourth with geometric analysis, and the fifth with geometric flows. These five volumes provide a condensed version of the Journal of Differential Geometry, helping readers to understand the development of the field of geometry over the past fifty years.
Author: Simon Donaldson
Publisher:
Published: 2017
Total Pages: 432
ISBN-13: 9781571463357
DOWNLOAD EBOOK →This volume presents twelve important papers on algebraic and complex geometry--papers that have played important roles in the development of these subjects. The subject matter ranges from the birational geometry of varieties, to geometric structures of moduli spaces in algebraic and complex geometry, to the geometry of compact and non-compact K�hler manifolds. Among the authors and topics are: Raoul Bott on a residue formula for holomorphic vector-fields; Armand Borel on metric properties of arithmetic quotients of symmetric spaces and an extension theorem; P. B. A. Kronheimer on Torelli-type theorem for gravitational instantons; Victor Guillemin on Kaehler structures on toric varieties; S. K. Donaldson on scalar curvature and stability of toric varieties; and Gang Liu on the volume growth of K�hler manifolds with nonnegative bisectional curvature. With a preface by Jun Li.
Author: Shing-Tung Yau
Publisher:
Published: 2018
Total Pages: 406
ISBN-13: 9781571463616
DOWNLOAD EBOOK →Author: Carolyn Farquhar Ulrich
Publisher:
Published: 1983*
Total Pages: 1114
ISBN-13:
DOWNLOAD EBOOK →Author: Guillermo Cortiñas
Publisher: American Mathematical Soc.
Published: 2012
Total Pages: 289
ISBN-13: 0821868640
DOWNLOAD EBOOK →Luis Santalo Winter Schools are organized yearly by the Mathematics Department and the Santalo Mathematical Research Institute of the School of Exact and Natural Sciences of the University of Buenos Aires (FCEN). This volume contains the proceedings of the third Luis Santalo Winter School which was devoted to noncommutative geometry and held at FCEN July 26-August 6, 2010. Topics in this volume concern noncommutative geometry in a broad sense, encompassing various mathematical and physical theories that incorporate geometric ideas to the study of noncommutative phenomena. It explores connections with several areas including algebra, analysis, geometry, topology and mathematical physics. Bursztyn and Waldmann discuss the classification of star products of Poisson structures up to Morita equivalence. Tsygan explains the connections between Kontsevich's formality theorem, noncommutative calculus, operads and index theory. Hoefel presents a concrete elementary construction in operad theory. Meyer introduces the subject of $\mathrm{C}^*$-algebraic crossed products. Rosenberg introduces Kasparov's $KK$-theory and noncommutative tori and includes a discussion of the Baum-Connes conjecture for $K$-theory of crossed products, among other topics. Lafont, Ortiz, and Sanchez-Garcia carry out a concrete computation in connection with the Baum-Connes conjecture. Zuk presents some remarkable groups produced by finite automata. Mesland discusses spectral triples and the Kasparov product in $KK$-theory. Trinchero explores the connections between Connes' noncommutative geometry and quantum field theory. Karoubi demonstrates a construction of twisted $K$-theory by means of twisted bundles. Tabuada surveys the theory of noncommutative motives.
Author: Anders Kock
Publisher: Cambridge University Press
Published: 2010
Total Pages: 317
ISBN-13: 0521116732
DOWNLOAD EBOOK →This elegant book is sure to become the standard introduction to synthetic differential geometry. It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or neighborhoods of the diagonal. These spaces enable a natural description of some of the basic constructions in local differential geometry and, in fact, form an inviting gateway to differential geometry, and also to some differential-geometric notions that exist in algebraic geometry. The presentation conveys the real strength of this approach to differential geometry. Concepts are clarified, proofs are streamlined, and the focus on infinitesimal spaces motivates the discussion well. Some of the specific differential-geometric theories dealt with are connection theory (notably affine connections), geometric distributions, differential forms, jet bundles, differentiable groupoids, differential operators, Riemannian metrics, and harmonic maps. Ideal for graduate students and researchers wishing to familiarize themselves with the field.