Showing papers on "Geometry and topology published in 1997"

Three-Dimensional Geometry and Topology

Abstract: Preface Reader's Advisory Ch. 1. What Is a Manifold? 3 Ch. 2. Hyperbolic Geometry and Its Friends 43 Ch. 3. Geometric Manifolds 109 Ch. 4. The Structure of Discrete Groups 209 Glossary 289 Bibliography 295 Index 301

Handbook of discrete and computational geometry

Abstract: COMBINATORIAL AND DISCRETE GEOMETRY Finite Point Configurations, J. Pach Packing and Covering, G. Fejes Toth Tilings, D. Schattschneider and M. Senechal Helly-Type Theorems and Geometric Transversals, R. Wenger Pseudoline Arrangements, J.E. Goodman Oriented Matroids, J. Richter-Gebert and G.M. Ziegler Lattice Points and Lattice Polytopes, A. Barvinok New! Low-Distortion Embeddings of Finite Metric Spaces, P. Indyk and J. Matousek New! Geometry and Topology of Polygonal Linkages, R. Connelly and E.D. Demaine New! Geometric Graph Theory, J. Pach Euclidean Ramsey Theory, R.L. Graham Discrete Aspects of Stochastic Geometry, R. Schneider Geometric Discrepancy Theory and Uniform Distribution, J.R. Alexander, J. Beck, and W.W.L. Chen Topological Methods, R.T. Zivaljevic Polyominoes, S.W. Golomb and D.A. Klarner POLYTOPES AND POLYHEDRA Basic Properties of Convex Polytopes, M. Henk, J. Richter-Gebert, and G.M. Ziegler Subdivisions and Triangulations of Polytopes, C.W. Lee Face Numbers of Polytopes and Complexes, L.J. Billera and A. Bjoerner Symmetry of Polytopes and Polyhedra, E. Schulte Polytope Skeletons and Paths, G. Kalai Polyhedral Maps, U. Brehm and E. Schulte ALGORITHMS AND COMPLEXITY OF FUNDAMENTAL GEOMETRIC OBJECTS Convex Hull Computations, R. Seidel Voronoi Diagrams and Delaunay Triangulations, S. Fortune Arrangements, D. Halperin Triangulations and Mesh Generation, M. Bern Polygons, J. O'Rourke and S. Suri Shortest Paths and Networks, J.S.B. Mitchell Visibility, J. O'Rourke Geometric Reconstruction Problems, S.S. Skiena New! Curve and Surface Reconstruction, T.K. Dey Computational Convexity, P. Gritzmann and V. Klee Computational Topology, G. Vegter Computational Real Algebraic Geometry, B. Mishra GEOMETRIC DATA STRUCTURES AND SEARCHING Point Location, J. Snoeyink New! Collision and Proximity Queries, M.C. Lin and D. Manocha Range Searching, P.K. Agarwal Ray Shooting and Lines in Space, M. Pellegrini Geometric Intersection, D.M. Mount New! Nearest Neighbors in High-Dimensional Spaces, P. Indyk COMPUTATIONAL TECHNIQUES Randomization and Derandomization, O. Cheong, K. Mulmuley, and E. Ramos Robust Geometric Computation, C.K. Yap Parallel Algorithms in Geometry, M.T. Goodrich Parametric Search, J.S. Salowe New! The Discrepancy Method in Computational Geometry, B. Chazelle APPLICATIONS OF DISCRETE AND COMPUTATIONAL GEOMETRY Linear Programming, M. Dyer, N. Megiddo, and E. Welzl Mathematical Programming, M.H. Todd Algorithmic Motion Planning, M. Sharir Robotics, D. Halperin, L.E. Kavraki, and J.-C. Latombe Computer Graphics, D. Dobkin and S. Teller New! Modeling Motion, L.J. Guibas Pattern Recognition, J. O'Rourke and G.T. Toussaint Graph Drawing, R. Tamassia and G. Liotta Splines and Geometric Modeling, C.L. Bajaj New! Surface Simplification and 3D Geometry Compression, J. Rossignac Manufacturing Processes, R. Janardan and T.C. Woo Solid Modeling, C.M. Hoffmann New! Computation of Robust Statistics: Depth, Median, and Related Measures, P.J. Rousseeuw and A. Struyf New! Geographic Information Systems, M. van Kreveld Geometric Application of the Grassmann-Cayley Algebra, N.L. White Rigidity and Scene Analysis, W. Whiteley Sphere Packing and Coding Theory, G.A. Kabatiansky and J.A. Rush Crystals and Quasicrystals, M. Senechal New! Biological Applications of Computational Topology, H. Edelsbrunner New! GEOMETRIC SOFTWARE Software, J. Joswig Two Computation Geometry Libraries: LEDA and CGAL, L. Kettner and S. Naher Index of Defined Terms New! Index of Cited Authors

Geometric Galois Actions: Esquisse d'un Programme

Abstract: Comme la conjoncture actuelle rend de plus en plus illusoire pour moi les perspectives d'un enseignement de recherche a l'Universite, je me suis resolu a demander mon admission au CNRS, pour pouvoir consacrer mon energie a developper des travaux et perspectives dont il devient clair qu'il ne se trouvera aucun eleve (ni meme, semble-t-il, aucun congenere mathematicien) pour les developper a ma place. En guise de document “Titres et Travaux”, on trouvera a la suite de ce texte la reproduction integrale d'une esquisse, par themes, de ce que je considerais comme mes principales contributions mathematiques au moment d'ecrire ce rapport, en 1972. Il contient egalement une liste d'articles publies a cette date. J'ai cesse toute publication d'articles scientifiques depuis 1970. Dans les lignes qui suivent, je me propose de donner un apercu au moins sur quelques themes principaux de mes reflexions mathematiques depuis lors. Ces reflexions se sont materialisees au cours des annees en deux volumineux cartons de notes manuscrites, difficilement dechiffrables sans doute a tout autre qu'a moi-meme, et qui, apres des stades de decantations successives, attendent leur heure peut-etre pour une redaction d'ensemble tout au moins provisoire, a l'intention de la communaute mathematique. Le terme “redaction” ici est quelque peu impropre, alors qu'il s'agit bien plus de developper des idees et visions multiples amorcees au cours de ces douze dernieres annees, en les precisant et les approfondissant, avec tous les rebondissements imprevus qui constamment accompagnent ce genre de travail – un travail de decouverte done, et non de compilation de notes pieusement accumulees.

Symplectic manifolds with no Kähler structure

Abstract: The starting point: Homotopy properties of kahler manifolds.- Nilmanifolds.- Solvmanifolds.- The examples of McDuff.- Symplectic structures in total spaces of bundles.- Survey.

Structure of dynamical systems : a symplectic view of physics

Abstract: The aim of this text is to treat all three basic theories of physics (classical, statistical and quantum mechanics) from the same perspective, namely that of symplectic geometry, in order to show the unifing power of the symplectic geometry approach. The book aims to give the reader an understanding of the interrelationships of the three basic theories of physics. The first two chapters give the necessary mathematical background in differential geometry, Lie groups, and symplectic geometry. In chapter three a symplectic description of Galilean and relativistic mechanics is given, culminating in the classification of elementary particles (relativistic and non-relativistic, with or without spin, with or without mass). In the fourth chapter statistic mechanics is put into symplectic form, finishing with a symplectic description of the kinetic theory of gases and the computation of specific heats. The final chapter covers the author's theory of geometric quantization, and included in this chapter are the derivations of the various wave equations, and the construction of the Fock space. This text is aimed at graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics and geometric quantization.

Geometry and topology of fracture systems

Abstract: Random three-dimensional fracture networks are generated according to various rules. Geometrical and topological features such as the number of three-dimensional blocks, the percolation thresholds and the cyclomatic numbers are studied with respect to fracture shapes and densities. All the results could be successfully interpreted by means of the excluded volume.

Geometry of Higher Dimensional Algebraic Varieties

Abstract: The subject of this book is the classification theory and geometry of higher dimensional varieties: existence and geometry of rational curves via characteristic p-methods, manifolds with negative Kodaira dimension, vanishing theorems, theory of extremal rays (Mori theory), and minimal models. The book gives a state-of-the-art intro- duction to a difficult and not readily accessible subject which has undergone enormous development in the last two decades. With no loss of precision, the volume focuses on the spread of ideas rather than on a deliberate inclusion of all proofs. The methods presented vary from complex analysis to complex algebraic geometry and algebraic geometry over fields of positive characteristics. The intended audience includes students in algebraic geometry and complex analysis as well as researchers in these fields and experts from other areas who wish to gain an overview of the theory.

Convergence Theorems in Riemannian Geometry

Abstract: This is a survey on the convergence theory developed rst by Cheeger and Gromov. In their theory one is concerned with the compactness of the class of riemannian manifolds with bounded curvature and lower bound on the injectivity radius. We explain and give proofs of almost all the major results, including Anderson's generalizations to the case where all one has is bounded Ricci curvature. The exposition is streamlined by the introduction of a norm for riemannian manifolds, which makes the theory more like that of Holder and Sobolev spaces.

Solitons, Geometry, and Topology: On the Crossroad

Abstract: Hyperelliptic Kleinian functions and applications by V. M. Buchstaber, V. Z. Enolskii, and D. V. Leikin Functionals of the Peierls-Frohlich type and the variational principle for the Whitham equations by B. Dubrovin Semiclassical motion of the electron. A proof of the Novikov conjecture in general position and counterexamples by I. A. Dynnikov An invariant of integral homology 3-spheres which is universal for all finite type invariants by T. Q. Le Krichever-Novikov algebras and the cohomology of the algebra of meromorphic vector fields by D. V. Millionshchikov Exactly solvable two-dimensional Schrodinger operators and Laplace transformations by S. P. Novikov and A. P. Veselov Modified Novikov-Veselov equation and differential geometry of surfaces by I. A. Taimanov Supermanifold forms and integration. A dual theory by T. Voronov On hyperplane sections of periodic surfaces by A. Zorich.

Symplectic geometry of plurisubharmonic functions

Abstract: In these lectures we describe symplectic geometry related to the notion of pseudo-convexity (or J-convexity). The notion of J-convexity, which is a complex analog of convexity, is one of the basic mathematical notions. Symplectic geometry built-in into this notion is essential for understanding the structure of affine (or Stein) complex manifolds. It plays also a major role in the classification of Stein complex structures up to deformation. Plurisubharmonic (or J-convex) functions on complex manifolds are analagous to convex functions on Riemannian manifolds but their theory is much richer. Symplectic geometry is crucial for understanding Morse-theoretic properties of J-convex functions.

Geometry, Combinatorial Designs and Related Structures: Difference sets: an update

Abstract: In the last few years there has been rapid progress in the theory of difference sets. This is a survey of these fascinating new developments.

Deformation Theory and Symplectic Geometry

Abstract: The first € price and the £ and $ price are net prices, subject to local VAT. Prices indicated with * include VAT for books; the €(D) includes 7% for Germany, the €(A) includes 10% for Austria. Prices indicated with ** include VAT for electronic products; 19% for Germany, 20% for Austria. All prices exclusive of carriage charges. Prices and other details are subject to change without notice. All errors and omissions excepted. D. Sternheimer, J. Rawnsley, S. Gutt (Eds.) Deformation Theory and Symplectic Geometry

Gauge theory and symplectic geometry

Abstract: Preface. Participants. Contributors. Lectures on Gauge Theory and Integrable Systems M. Audin. Symplectic Geometry of Plurisubharmonic Functions Y. Eliashberg. Frobenius Manifolds N. Hitchin. Moduli Spaces and Particle Spaces J. Hurtubise. J-Holomorphic Curves and Symplectic Invariants F. Lalonde. Lectures on Gromov Invariants for Symplectic 4-Manifolds D. McDuff. Index.

Geometrically Finite Complex Hyperbolic Manifolds

Abstract: The aim of this paper is to study geometry and topology of geometrically finite complex hyperbolic manifolds, especially their ends, as well as geometry of their holonomy groups. This study is based on our structural theorem for discrete groups acting on Heisenberg groups, on the fiber bundle structure of Heisenberg manifolds, and on the existence of finite coverings of a geometrically finite manifold such that their parabolic ends have either Abelian or 2-step nilpotent holonomy. We also study an interplay between Kahler geometry of complex hyperbolic n-manifolds and Cauchy–Riemannian geometry of their boundary (2n-1)-manifolds at infinity, and this study is based on homotopy equivalence of manifolds and isomorphism of fundamental groups.