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C*-algebras and Elliptic Theory
This volume contains the proceedings of the conference on "C*-algebras and Elliptic Theory" held in Bedlewo, Poland, in February 2004. It consists of original research papers and expository articles focussing on index theory and topology of manifolds.The collection offers a cross-section of significant recent advances in several fields, the main subject being K-theory (of C*-algebras, equivariant K-theory). A number of papers is related to the index theory of pseudodifferential operators on singular manifolds (with boundaries, corners) or open manifolds. Further topics are Hopf cyclic cohomology, geometry of foliations, residue theory, Fredholm pairs and others.
Braid Groups
Braids and braid groups have been at the heart of mathematical development over the last two decades. Braids play an important role in diverse areas of mathematics and theoretical physics. The special beauty of the theory of braids stems from their attractive geometric nature and their close relations to other fundamental geometric objects, such as knots, links, mapping class groups of surfaces, and configuration spaces. In this presentation the authors thoroughly examine various aspects of the theory of braids, starting from basic definitions and then moving to more recent results. The advanced topics cover the Burau and the Lawrence--Krammer--Bigelow representations of the braid groups, the Alexander--Conway and Jones link polynomials, connections with the representation theory of the Iwahori--Hecke algebras, and the Garside structure and orderability of the braid groups.
Axiom of Choice
AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom, shunned by some, used indiscriminately by others. This treatise shows paradigmatically that:Disasters happen without AC: Many fundamental mathematical results fail (being equivalent in ZF to AC or to some weak form of AC).Disasters happen with AC: Many undesirable mathematical monsters are being created (e.g., non measurable sets and undeterminate games).Illuminating examples are drawn from diverse areas of mathematics, particularly from general topology, but also from algebra, order theory, elementary analysis, measure theory, game theory, and graph theory.
Analytical and Numerical Approaches to Mathematical Relativity
This book contains a representative collection of surveys by experts in mathematical relativity writing about the current status of, and problems in, their fields. There are four contributions for each of the following mathematical areas: differential geometry and differential topology, analytical methods and differential equations, and numerical methods. This book addresses graduate students and specialist researchers alike.
An Invitation to Morse Theory
This treatment of Morse Theory focuses on applications and is intended for a graduate course on differential or algebraic topology. This is the first textbook to include topics such as Morse-Smale flows, min-max theory, moment maps and equivariant cohomology, and complex Morse theory.
An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem
This book provides an introduction to the basics of sub-Riemannian differential geometry and geometric analysis in the Heisenberg group, focusing primarily on the current state of knowledge regarding Pierre Pansu's celebrated 1982 conjecture regarding the sub-Riemannian isoperimetric profile.
An Introduction to Structural Optimization
This textbook gives an introduction to all three classes of geometry optimization problems of mechanical structures: sizing, shape and topology optimization. The style is explicit and concrete, focusing on problem formulations and numerical solution methods. The treatment is detailed enough to enable readers to write their own implementations. On the book's homepage, programs may be downloaded that further facilitate the learning of the material covered.
An Introduction to Manifolds
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.
Algorithmic topology and classification of 3-manifolds
This book provides a comprehensive and detailed account of different topics in algorithmic 3-dimensional topology. The book is intended to combine the pedagogical approach of a graduate textbook with the completeness and reliability of a research monograph.
Algebraic Geometry and Geometric Modeling
Algebraic Geometry provides an impressive theory targeting the understanding of geometric objects defined algebraically. Geometric Modeling uses every day, in order to solve practical and difficult problems, digital shapes based on algebraic models. In this book, we have collected articles bridging these two areas. The confrontation of the different points of view results in a better analysis of what the key challenges are and how they can be met. We focus on the following important classes of problems: implicitization, classification, and intersection. The combination of illustrative pictures, explicit computations and review articles will help the reader to handle these subjects.
Algebraic Cycles, Sheaves, Shtukas, and Moduli : Impanga Lecture Notes
The articles in this volume are devoted to: - moduli of coherent sheaves. - principal bundles and sheaves and their moduli. - new insights into Geometric Invariant Theory. - stacks of shtukas and their compactifications. - algebraic cycles vs. commutative algebra. - Thom polynomials of singularities. - zero schemes of sections of vector bundles.
Ad-Hoc Networking Towards Seamless Communications
Ad-Hoc Networking Towards Seamless Communications is dedicated to an area that attracts growing interest in academia and industry and concentrates on wireless ad hoc networking paradigm. The persistent efforts to acquire the ability to establish dynamic wireless connections from anywhere to anyone with any device without prerequisite imbedded infrastructure move the communications boundaries towards ad-hoc networks. Recently, ad hoc networking has attracted growing interest due to advances in wireless communications, and developed framework for running IP based protocols. The expected degree of penetration of these networks will depend on the successful resolution of the key features.
Active Sensor Planning for Multiview Vision Tasks
The book describes some effective strategies to generate a sequence of viewing poses and sensor settings for optimally completing a perception task. Several methods are proposed to solve the problems in both model-based and nonmodel-based vision tasks. For model-based applications, the method involves determination of the optimal sensor placements and a shortest path through these viewpoints for automatic generation of a perception plan.
A Taste of Topology
The present book grew out of notes for an introductory topology course at the University of Alberta. It provides a concise introduction to set-theoretic topology (and to a tiny little bit of algebraic topology). Great care has been devoted to the selection of examples that are not self-serving, but already accessible for students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis.
A Geometry of Approximation : Rough Set Theory: Logic, Algebra and Topology of Conceptual Patterns
A Geometry of Approximation' addresses Rough Set Theory, a field of interdisciplinary research first proposed by Zdzislaw Pawlak in 1982, and focuses mainly on its logic-algebraic interpretation. The theory is embedded in a broader perspective that includes logical and mathematical methodologies pertaining to the theory, as well as related epistemological issues. Any mathematical technique that is introduced in the book is preceded by logical and epistemological explanations. Intuitive justifications are also provided, insofar as possible, so that the general perspective is not lost.
