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Author : Victor Guillemin,Shlomo Sternberg
Publisher : American Mathematical Soc.
Page : 80 pages
File Size : 53,6 Mb
Release : 1966
Category : Mathematics
ISBN : 9780821812648
Author : Michiel Hazewinkel,Murray Gerstenhaber
Publisher : Springer Science & Business Media
Page : 1024 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400930575
This volume is a result of a meeting which took place in June 1986 at 'll Ciocco" in Italy entitled 'Deformation theory of algebras and structures and applications'. It appears somewhat later than is perhaps desirable for a volume resulting from a summer school. In return it contains a good many results which were not yet available at the time of the meeting. In particular it is now abundantly clear that the Deformation theory of algebras is indeed central to the whole philosophy of deformations/perturbations/stability. This is one of the main results of the 254 page paper below (practically a book in itself) by Gerstenhaber and Shack entitled "Algebraic cohomology and defor mation theory". Two of the main philosphical-methodological pillars on which deformation theory rests are the fol lowing • (Pure) To study a highly complicated object, it is fruitful to study the ways in which it can arise as a limit of a family of simpler objects: "the unraveling of complicated structures" . • (Applied) If a mathematical model is to be applied to the real world there will usually be such things as coefficients which are imperfectly known. Thus it is important to know how the behaviour of a model changes as it is perturbed (deformed).
Author : Constantin Neophytos Kockinos
Publisher : Unknown
Page : 504 pages
File Size : 51,5 Mb
Release : 1974
Category : Jets (Topology)
ISBN : STANFORD:36105011768053
Author : Antonio Kumpera,Donald Clayton Spencer,Université de Montréal. Département de mathématiques
Publisher : Presses de l'Université de Montréal
Page : 108 pages
File Size : 46,5 Mb
Release : 1974
Category : Differential equations, Linear
ISBN : UOM:39015039390003
The main goal of these notes is the description of a non-linear complex into which the integrability (or compatibility) condition is inserted as a non-linear operator in such a way that exactness implies the integrability of the almost-structure (existence of local coordinates for the structure) or, by the introduction of parameters, the existence of a (germ of) deformation of the structure. To the non-linear complex are attached some fundamental identities and a structure equation. The non-linear complex is a finite form of the initial portion of a linear complex which is a differential graded Lie algebra. The operators in the non-linear and linear complexes are of first order.
Author : Kenji Ueno,Yūji Shimizu
Publisher : American Mathematical Soc.
Page : 328 pages
File Size : 42,9 Mb
Release : 2002
Category : Mathematics
ISBN : 0821821563
The word ``moduli'' in the sense of this book first appeared in the epoch-making paper of B. Riemann, Theorie der Abel'schen Funktionen, published in 1857. Riemann defined a Riemann surface of an algebraic function field as a branched covering of a one-dimensional complex projective space, and found out that Riemann surfaces have parameters. This work gave birth to the theory of moduli. However, the viewpoint regarding a Riemann surface as an algebraic curve became the mainstream,and the moduli meant the parameters for the figures (graphs) defined by equations. In 1913, H. Weyl defined a Riemann surface as a complex manifold of dimension one. Moreover, Teichmuller's theory of quasiconformal mappings and Teichmuller spaces made a start for new development of the theory ofmoduli, making possible a complex analytic approach toward the theory of moduli of Riemann surfaces. This theory was then investigated and made complete by Ahlfors, Bers, Rauch, and others. However, the theory of Teichmuller spaces utilized the special nature of complex dimension one, and it was difficult to generalize it to an arbitrary dimension in a direct way. It was Kodaira-Spencer's deformation theory of complex manifolds that allowed one to study arbitrary dimensional complex manifolds.Initial motivation in Kodaira-Spencer's discussion was the need to clarify what one should mean by number of moduli. Their results, together with further work by Kuranishi, provided this notion with intrinsic meaning. This book begins by presenting the Kodaira-Spencer theory in its original naiveform in Chapter 1 and introduces readers to moduli theory from the viewpoint of complex analytic geometry. Chapter 2 briefly outlines the theory of period mapping and Jacobian variety for compact Riemann surfaces, with the Torelli theorem as a goal. The theory of period mappings for compact Riemann surfaces can be generalized to the theory of period mappings in terms of Hodge structures for compact Kahler manifolds. In Chapter 3, the authors state the theory of Hodge structures, focusingbriefly on period mappings. Chapter 4 explains conformal field theory as an application of moduli theory. This is the English translation of a book originally published in Japanese. Other books by Kenji Ueno published in this AMS series, Translations of Mathematical Monographs, include An Introduction toAlgebraic Geometry, Volume 166, Algebraic Geometry 1: From Algebraic Varieties to Schemes, Volume 185, and Algebraic Geometry 2: Sheaves and Cohomology, Volume 197.
Author : Michiel Hazewinkel
Publisher : Springer
Page : 732 pages
File Size : 41,9 Mb
Release : 2013-12-20
Category : Mathematics
ISBN : 9789400959835
Author : Donald Clayton Spencer
Publisher : Unknown
Page : 32 pages
File Size : 41,8 Mb
Release : 1962
Category : Pseudogroup structures, Deformation of
ISBN : STANFORD:36105031331999
Author : M. Hazewinkel
Publisher : Springer
Page : 932 pages
File Size : 54,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781489937919
Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 982 pages
File Size : 50,8 Mb
Release : 1994-02-28
Category : Mathematics
ISBN : 1556080107
The Encyclopaedia of Mathematics is the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics which exists today. With over 7,000 articles from `A-integral' to `Zygmund Class of Functions', supplemented with a wealth of complementary information, and an index volume providing thorough cross-referencing of entries of related interest, the Encyclopaedia of Mathematics offers an immediate source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods. The depth and breadth of content and the straightforward, careful presentation of the information, with the emphasis on accessibility, makes the Encyclopaedia of Mathematics an immensely useful tool for all mathematicians and other scientists who use, or are confronted by, mathematics in their work. The Enclyclopaedia of Mathematics provides, without doubt, a reference source of mathematical knowledge which is unsurpassed in value and usefulness. It can be highly recommended for use in libraries of universities, research institutes, colleges and even schools.
Author : Marie-Paule Malliavin
Publisher : Springer
Page : 280 pages
File Size : 44,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540475927
These proceedings reflect the main activities of the Paris Séminaire d'Algèbre 1989-1990, with a series of papers in Invariant Theory, Representation Theory and Combinatorics. It contains original works from J. Dixmier, F. Dumas, D. Krob, P. Pragacz and B.J. Schmid, as well as a new presentation of Derived Categories by J.E. Björk and as introduction to the deformation theory of Lie equations by J.F. Pommaret. J. Dixmier: Sur les invariants du groupe symétrique dans certaines représentations II.- B.J. Schmid: Finite groups and invariant theory.- J.E. Björk: Derived categories.- P. Pragacz: Algebro-Geometric applications of Schur S- and Q-polynomials.- F. Dumas: Sous-corps de fractions rationnelles des corps gauches de séries de Laurent.- D. Krob: Expressions rationnelles sur un anneau.- J.F. Pommaret: Deformation theory of algebraic and Geometric structures.- M. van den Bergh: Differential operators on semi-invariants for tori and weighted projective spaces.
Author : Donald Clayton Spencer,Shokichi Iyanaga
Publisher : Princeton University Press
Page : 423 pages
File Size : 45,6 Mb
Release : 2015-03-08
Category : Mathematics
ISBN : 9781400871230
Global analysis describes diverse yet interrelated research areas in analysis and algebraic geometry, particularly those in which Kunihiko Kodaira made his most outstanding contributions to mathematics. The eminent contributors to this volume, from Japan, the United States, and Europe, have prepared original research papers that illustrate the progress and direction of current research in complex variables and algebraic and differential geometry. The authors investigate, among other topics, complex manifolds, vector bundles, curved 4-dimensional space, and holomorphic mappings. Bibliographies facilitate further reading in the development of the various studies. Originally published in 1970. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author : Donald Clayton Spencer
Publisher : World Scientific
Page : 694 pages
File Size : 44,6 Mb
Release : 1985
Category : Mathematics
ISBN : 9971978032
Author : Rene Thom
Publisher : CRC Press
Page : 404 pages
File Size : 41,8 Mb
Release : 2018-03-05
Category : Mathematics
ISBN : 9780429961571
First Published in 2018. Routledge is an imprint of Taylor & Francis, an Informa company.
Author : Louis R. Hunt,Clyde Martin
Publisher : Unknown
Page : 466 pages
File Size : 43,8 Mb
Release : 1984
Category : Science
ISBN : 0915692376
Author : J. F. Pommaret
Publisher : CRC Press
Page : 428 pages
File Size : 49,7 Mb
Release : 1978
Category : Mathematics
ISBN : 067700270X
