Philippe Tondeur's Books

Geometry of Foliations

By: Philippe Tondeur

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Surveys research over the past few years at a level accessible to graduate students and researchers with a background in differential and Riemannian geometry. Among the topics are foliations of codimension one, holonomy, Lie foliations, basic forms, mean curvature, the Hodge theory for the transversal Laplacian, applications of the heat equation method to Riemannian foliations, the spectral theory, Connes' perspective of foliations as examples of non- commutative spaces, and infinite-dimensional examples. The bibliographic appendices list books and surveys on particular aspects of foliations, proceedings of conferences and symposia, all papers on the subject up to 1995, and the numbers of papers published on the subject during the years 1990-95. Annotation copyrighted by Book News, Inc., Portland, OR

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Page Count

330

Publisher

Springer Science & Business Media

Published Date

ISBN 10

376435741X

ISBN 13

9783764357412

Collected Papers of K.T. Chen

By: Kuo-Tsai Chen,Philippe Tondeur

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Collected Papers of K.T. Chen

By: Kuo-Tsai Chen,Philippe Tondeur

Kuo-Tsai Chen (1923-1987) is best known to the mathematics community for his work on iterated integrals and power series connections in conjunction with his research on the cohomology of loop spaces. His work is intimately related to the theory of minimal models as developed by Dennis Sullivan, whose own work was in part inspired by the research of Chen. An outstanding and original mathematician, Chen's work falls naturally into three periods: his early work on group theory and links in the three sphere; his subsequent work on formal differential equations, which gradually developed into his most powerful and important work; and his work on iterated integrals and homotopy theory, which occupied him for the last twenty years of his life. The goal of Chen's iterated integrals program, which is a de Rham theory for path spaces, was to study the interaction of topology and analysis through path integration. The present volume is a comprehensive collection of Chen's mathematical publications preceded by an article, "The Life and Work of Kuo-Tsai Chen," placing his work and research interests into their proper context and demonstrating the power and scope of his influence.

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776

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Springer Science & Business Media

Published Date

ISBN 10

0817640053

ISBN 13

9780817640057

Foliations on Riemannian Manifolds

By: Philippe Tondeur

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Foliations on Riemannian Manifolds

By: Philippe Tondeur

A first approximation to the idea of a foliation is a dynamical system, and the resulting decomposition of a domain by its trajectories. This is an idea that dates back to the beginning of the theory of differential equations, i.e. the seventeenth century. Towards the end of the nineteenth century, Poincare developed methods for the study of global, qualitative properties of solutions of dynamical systems in situations where explicit solution methods had failed: He discovered that the study of the geometry of the space of trajectories of a dynamical system reveals complex phenomena. He emphasized the qualitative nature of these phenomena, thereby giving strong impetus to topological methods. A second approximation is the idea of a foliation as a decomposition of a manifold into submanifolds, all being of the same dimension. Here the presence of singular submanifolds, corresponding to the singularities in the case of a dynamical system, is excluded. This is the case we treat in this text, but it is by no means a comprehensive analysis. On the contrary, many situations in mathematical physics most definitely require singular foliations for a proper modeling. The global study of foliations in the spirit of Poincare was begun only in the 1940's, by Ehresmann and Reeb.

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258

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Springer Science & Business Media

Published Date

ISBN 10

1461387809

ISBN 13

9781461387800

Encyclopedia of French Film Directors

By: Philippe Rège

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Encyclopedia of French Film Directors

By: Philippe Rège

Cinema has been long associated with France, dating back to 1895, when Louis and Auguste Lumi_re screened their works, the first public viewing of films anywhere. Early silent pioneers Georges MZli_s, Alice Guy BlachZ and others followed in the footsteps of the Lumi_re brothers and the tradition of important filmmaking continued throughout the 20th century and beyond. In Encyclopedia of French Film Directors, Philippe Rège identifies every French director who has made at least one feature film since 1895. From undisputed masters to obscure one-timers, nearly 3,000 directors are cited here, including at least 200 filmmakers not mentioned in similar books published in France. Each director's entry contains a brief biographical summary, including dates and places of birth and death; information on the individual's education and professional training; and other pertinent details, such as real names (when the filmmaker uses a pseudonym). The entries also provide complete filmographies, including credits for feature films, shorts, documentaries, and television work. Some of the most important names in the history of film can be found in this encyclopedia, from masters of the Golden Age_Jean Renoir and RenZ Clair_to French New Wave artists such as Fran_ois Truffaut and Jean-Luc Godard.

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1486

Publisher

Scarecrow Press

Published Date

ISBN 10

081086939X

ISBN 13

9780810869394

Invariant Differential Operators and the Cohomology of Lie Algebra Sheaves

By: Franz W. Kamber,Philippe Tondeur

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Invariant Differential Operators and the Cohomology of Lie Algebra Sheaves

By: Franz W. Kamber,Philippe Tondeur

For a Lie algebra sheaf L of derivations of a sheaf of rings O on a space X global cohomology groups and local cohomology sheaves are introduced and analyzed. Global and local splitting obstructions for extensions of modules over a Lie algebra sheaf are studied. In the applications considered, L is a Lie algebra sheaf of vector fields on a manifold M, O the structure sheaf of M. For vector bundles E, F on M on which L acts, the existence of invariant differential operators D: E→F whose symbols are preassigned equivariant maps is discussed in terms of these splitting obstructions. Lie algebra sheaves defined by Lie group actions are considered. This theory is applied in particular to the case of a transitive L. The splitting obstructions for extensions of modules over a transitive Lie algebra sheaf are analyzed in detail. The results are then applied to the problem of the existence of invariant connections on locally homogeneous spaces. The obstruction is computed in some examples.

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