In this work, whose text is in French, the author defines and studies a Reidemeister torsion for hyperbolic three-dimensional manifolds of finite volume. This torsion is an invariant obtained from the combinatorial and the hyperbolic structures of the manifold, and it is studied for closed manifolds and orbifolds, cusped and cone manifolds. The author includes several examples and studies the main properties, involving many aspects of hyperbolic three-manifolds. In particular, it is shown that the torsion of hyperbolic cone manifolds tends to zero for Euclidean degenerations.

This book is intended for graduate students and research mathematicians.

This volume gives two new methods for constructing $p$-elementary Hopf algebra orders over the valuation ring $R$ of a local field $K$ containing the $p$-adic rational numbers. One method constructs Hopf orders using isogenies of commutative degree 2 polynomial formal groups of dimension $n$, and is built on a systematic study of such formal group laws. The other method uses an exponential generalization of a 1992 construction of Greither. Both constructions yield Raynaud orders as iterated extensions of rank $p$ Hopf algebras; the exponential method obtains all Raynaud orders whose...

This volume develops a systematic study of time-dependent control processes. The basic problem of null controllability of linear systems is first considered. Using methods of ergodic theory and topological dynamics, general local null controllability criteria are given. Then the subtle question of global null controllability is studied. Next, the random linear feedback and stabilization problem is posed and solved. Using concepts of exponential dichotomy and rotation number for linear Hamiltonian systems, a solution of the Riccati equation is obtained which has extremely good robustness...

This work provides a unified way of looking at the apparently sporadic Weyl groups connected with the classical algebraic geometry of surfaces from the viewpoint of the recently established Minimal Model Program for 3-folds (Mori's Program). Matsuki explores the correspondence between the algebraic objects (the Weyl chambers, roots, reflections) and geometric objects (the ample cones of minimal models, extremal rays, flops) for the Weyl groups appearing with rational double points, Kodaira-type degenerations of elliptic curves and K3 surfaces. A complete table for all the extremal rays of...

Subdivision methods in computer graphics constitute a large class of recursive schemes for computing curves and surfaces. They seem to have their origin in the geometric problem of smoothing the corners of a given polyhedral surface - in fact, these methods are sometimes called wood carver algorithms because the repeated smoothing operations are analogous to sculpting wood. This book presents a systematic development of the basic mathematical principles and concepts associated with stationary subdivision algorithms. The authors pay special attention to the structure of such algorithms in a...

This volume studies the behaviour of a random heat kernel associated with a stochastic partial differential equation, and gives short-time expansion of this heat kernel. The author finds that the dominant exponential term is classical and depends only on the Riemannian distance function. The second exponential term is a work term and also has classical meaning. There is also a third non-negligible exponential term which blows up. The author finds an expression for this third exponential term which involves a random translation of the index form and the equations of Jacobi fields. In the...

Concerned with the calculation of the cohomology of the mapping class group of a closed oriented surface of genus two, this book uses methods involving braid groups, modular representations of symmetric groups and configuration spaces.

This book presents a survey of some recent developments in an important subfield of the new subject of anticipative stochastic analysis. D. Nualart and E. Pardoux have developed into a practicable calculus the theory of stochastic integration of processes not necessarily adapted to the driving Wiener process. This leads to anticipative stochastic differential equations with Skorohod integral and to anticipative Girsanov transformations, both of which are studied in the present work. The anticipative Girsanov transformations constitute the main tool for tackling stochastic differential...