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| Author | : Georges De Rham |
| Publisher | : |
| Total Pages | : 124 |
| Release | : 2013-02 |
| Genre | : |
| ISBN | : 9781258578343 |
Lectures Delivered In A Seminar Conducted By Professors Hermann Weyl And Karl Ludwig Siegel At The Institute For Advanced Study, 1950.
| Author | : André Haefliger |
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| Total Pages | : |
| Release | : 1970 |
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| Author | : Andre Haefliger |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 267 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642491979 |
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Profiles Swiss mathematician Georges de Rham (1903-1990), with information provided as part of the MacTutor History of Mathematics Archive of the University of Saint Andrews School of Mathematics and Statistics in Scotland. Describes the de Rahm theorem and other contributions of Rham to the field of geometry.
| Author | : Georges de Rham |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 178 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642617522 |
In this work, I have attempted to give a coherent exposition of the theory of differential forms on a manifold and harmonic forms on a Riemannian space. The concept of a current, a notion so general that it includes as special cases both differential forms and chains, is the key to understanding how the homology properties of a manifold are immediately evident in the study of differential forms and of chains. The notion of distribution, introduced by L. Schwartz, motivated the precise definition adopted here. In our terminology, distributions are currents of degree zero, and a current can be considered as a differential form for which the coefficients are distributions. The works of L. Schwartz, in particular his beautiful book on the Theory of Distributions, have been a very great asset in the elaboration of this work. The reader however will not need to be familiar with these. Leaving aside the applications of the theory, I have restricted myself to considering theorems which to me seem essential and I have tried to present simple and complete of these, accessible to each reader having a minimum of mathematical proofs background. Outside of topics contained in all degree programs, the knowledge of the most elementary notions of general topology and tensor calculus and also, for the final chapter, that of the Fredholm theorem, would in principle be adequate.
| Author | : Loring W. Tu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 426 |
| Release | : 2010-10-05 |
| Genre | : Mathematics |
| ISBN | : 1441974008 |
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
| Author | : Eduardo Cattani |
| Publisher | : Princeton University Press |
| Total Pages | : 607 |
| Release | : 2014-07-21 |
| Genre | : Mathematics |
| ISBN | : 0691161348 |
This book provides a comprehensive and up-to-date introduction to Hodge theory—one of the central and most vibrant areas of contemporary mathematics—from leading specialists on the subject. The topics range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps. Of particular interest is the study of algebraic cycles, including the Hodge and Bloch-Beilinson Conjectures. Based on lectures delivered at the 2010 Summer School on Hodge Theory at the ICTP in Trieste, Italy, the book is intended for a broad group of students and researchers. The exposition is as accessible as possible and doesn't require a deep background. At the same time, the book presents some topics at the forefront of current research. The book is divided between introductory and advanced lectures. The introductory lectures address Kähler manifolds, variations of Hodge structure, mixed Hodge structures, the Hodge theory of maps, period domains and period mappings, algebraic cycles (up to and including the Bloch-Beilinson conjecture) and Chow groups, sheaf cohomology, and a new treatment of Grothendieck’s algebraic de Rham theorem. The advanced lectures address a Hodge-theoretic perspective on Shimura varieties, the spread philosophy in the study of algebraic cycles, absolute Hodge classes (including a new, self-contained proof of Deligne’s theorem on absolute Hodge cycles), and variation of mixed Hodge structures. The contributors include Patrick Brosnan, James Carlson, Eduardo Cattani, François Charles, Mark Andrea de Cataldo, Fouad El Zein, Mark L. Green, Phillip A. Griffiths, Matt Kerr, Lê Dũng Tráng, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu.
| Author | : Robert Hooke |
| Publisher | : Routledge |
| Total Pages | : 424 |
| Release | : 2014-09-11 |
| Genre | : History |
| ISBN | : 1136230297 |
Shortly after Hooke died in 1703, his miscellaneous papers and unpublished manuscripts were entrusted to Richard Waller, who edited and published some of them in a volume titled The Posthumous Works of Robert Hooke (1705; reprinted, Frank Cass, 1968). Waller himself died, however, before he was able to complete the task of republishing Hooke’s papers and they were eventually handed on to William Derham. After delaying for what some of Hooke’s followers thought to be a scandalously long time, Derham finally published this volume in 1726. It contains numerous papers and notes by Hooke as well as a number of important papers and letters written by Hooke’s contemporaries and found, evidently, among Hooke’s literary remains. This is an exact facsimile reproduction of Derham’s edition of the Philosophical experiments and Observations of the late Eminent Dr. Rober Hooke (1726) except that an analytical table of contents, prepared by the General Editor, has been added. First Published in 1967. Routledge is an imprint of Taylor & Francis, an informa company.
| Author | : John M. Lee |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 646 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 0387217525 |
Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why
| Author | : Patrick Popescu-Pampu |
| Publisher | : Springer |
| Total Pages | : 181 |
| Release | : 2016-08-26 |
| Genre | : Mathematics |
| ISBN | : 3319423126 |
Exploring several of the evolutionary branches of the mathematical notion of genus, this book traces the idea from its prehistory in problems of integration, through algebraic curves and their associated Riemann surfaces, into algebraic surfaces, and finally into higher dimensions. Its importance in analysis, algebraic geometry, number theory and topology is emphasized through many theorems. Almost every chapter is organized around excerpts from a research paper in which a new perspective was brought on the genus or on one of the objects to which this notion applies. The author was motivated by the belief that a subject may best be understood and communicated by studying its broad lines of development, feeling the way one arrives at the definitions of its fundamental notions, and appreciating the amount of effort spent in order to explore its phenomena.
