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Author: Antonio Kumpera
Publisher: Presses de l'Université de Montréal
ISBN:
Category : Differential equations, Linear
Languages : en
Pages : 108
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Book Description
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: Antonio Kumpera
Publisher: Presses de l'Université de Montréal
ISBN:
Category : Differential equations, Linear
Languages : en
Pages : 108
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Book Description
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: Victor Guillemin
Publisher: American Mathematical Soc.
ISBN: 0821812645
Category : Geometry, Differential
Languages : en
Pages : 90
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Book Description
Author: Donald Clayton Spencer
Publisher: World Scientific
ISBN: 9789971978044
Category : Mathematics
Languages : en
Pages : 460
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Book Description
Author: J. F. Pommaret
Publisher: CRC Press
ISBN: 9780677002705
Category : Mathematics
Languages : en
Pages : 428
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Book Description
Author: Antonio Kumpera
Publisher: Princeton University Press
ISBN: 1400881730
Category : Mathematics
Languages : en
Pages : 309
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Book Description
In this monograph the authors redevelop the theory systematically using two different approaches. A general mechanism for the deformation of structures on manifolds was developed by Donald Spencer ten years ago. A new version of that theory, based on the differential calculus in the analytic spaces of Grothendieck, was recently given by B. Malgrange. The first approach adopts Malgrange's idea in defining jet sheaves and linear operators, although the brackets and the non-linear theory arc treated in an essentially different manner. The second approach is based on the theory of derivations, and its relationship to the first is clearly explained. The introduction describes examples of Lie equations and known integrability theorems, and gives applications of the theory to be developed in the following chapters and in the subsequent volume.
Author: Michiel Hazewinkel
Publisher: Springer Science & Business Media
ISBN: 9400930577
Category : Mathematics
Languages : en
Pages : 1024
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Book Description
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:
ISBN:
Category : Jets (Topology)
Languages : en
Pages : 504
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Book Description
Author: Shlomo Sternberg
Publisher: American Mathematical Soc.
ISBN: 0821813854
Category : Mathematics
Languages : en
Pages : 466
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Book Description
This book is based on lectures given at Harvard University during the academic year 1960-1961. The presentation assumes knowledge of the elements of modern algebra (groups, vector spaces, etc.) and point-set topology and some elementary analysis. Rather than giving all the basic information or touching upon every topic in the field, this work treats various selected topics in differential geometry. The author concisely addresses standard material and spreads exercises throughout the text. His reprint has two additions to the original volume: a paper written jointly with V. Guillemin at the beginning of a period of intense interest in the equivalence problem and a short description from the author on results in the field that occurred between the first and the second printings.
Author: M. A. Akivis
Publisher: American Mathematical Soc.
ISBN: 0821853554
Category : Mathematics
Languages : en
Pages : 334
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Book Description
This book describes the life and achievements of the great French mathematician, Elie Cartan. Here readers will find detailed descriptions of Cartan's discoveries in Lie groups and algebras, associative algebras, differential equations, and differential geometry, as well of later developments stemming from his ideas. There is also a biographical sketch of Cartan's life. A monumental tribute to a towering figure in the history of mathematics, this book will appeal to mathematicians and historians alike.
Author: Donald Clayton Spencer
Publisher: Princeton University Press
ISBN: 1400871239
Category : Mathematics
Languages : en
Pages : 423
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Book Description
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.
