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Geometry And Topology Of Configuration Spaces

Author: Edward R. Fadell
Publisher: Springer Science & Business Media
ISBN: 3642564461
Size: 30.74 MB
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With applications in mind, this self-contained monograph provides a coherent and thorough treatment of the configuration spaces of Euclidean spaces and spheres, making the subject accessible to researchers and graduates with a minimal background in classical homotopy theory and algebraic topology.

The Influence Of Solomon Lefschetz In Geometry And Topology

Author: Ernesto Lupercio
Publisher: American Mathematical Soc.
ISBN: 0821894943
Size: 18.18 MB
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The influence of Solomon Lefschetz (1884-1972) in geometry and topology 40 years after his death has been very profound. Lefschetz's influence in Mexican mathematics has been even greater. In this volume, celebrating 50 years of mathematics at Cinvestav-México, many of the fields of geometry and topology are represented by some of the leaders of their respective fields. This volume opens with Michael Atiyah reminiscing about his encounters with Lefschetz and México. Topics covered in this volume include symplectic flexibility, Chern-Simons theory and the theory of classical theta functions, toric topology, the Beilinson conjecture for finite-dimensional associative algebras, partial monoids and Dold-Thom functors, the weak b-principle, orbit configuration spaces, equivariant extensions of differential forms for noncompact Lie groups, dynamical systems and categories, and the Nahm pole boundary condition.

Noncompact Problems At The Intersection Of Geometry Analysis And Topology

Author: Haim Brézis
Publisher: American Mathematical Soc.
ISBN: 0821836358
Size: 68.27 MB
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This proceedings volume contains articles from the conference held at Rutgers University in honor of Haim Brezis and Felix Browder, two mathematicians who have had a profound impact on partial differential equations, functional analysis, and geometry. The material is suitable for graduate students and researchers interested in problems in analysis and differential equations on noncompact manifolds.

Braids

Author: A. Jon Berrick
Publisher: World Scientific
ISBN: 9814291412
Size: 23.99 MB
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This book is an indispensable guide for anyone seeking to familarize themselves with research in braid groups, configuration spaces and their applications. Starting at the beginning, and assuming only basic topology and group theory, the volume''s noted expositors take the reader through the fundamental theory and on to current research and applications in fields as varied as astrophysics, cryptography and robotics. As leading researchers themselves, the authors write enthusiastically about their topics, and include many striking illustrations. The chapters have their origins in tutorials given at a Summer School on Braids, at the National University of Singapore''s Institute for Mathematical Sciences in June 2007, to an audience of more than thirty international graduate students. Sample Chapter(s). Foreword (31 KB). Chapter 1: Tutorial on the Braid Groups (372 KB). Contents: Tutorial on the Braid Groups (D Rolfsen); Simplicial Objects and Homotopy Groups (J Wu); Introduction to Configuration Spaces and Their Applications (F R Cohen); Configuration Spaces, Braids, and Robotics (R Ghrist); Braids and Magnetic Fields (M A Berger); Braid Group Cryptography (D Garber). Readership: Graduates and researchers in mathematics (low-dimensional topology, homotopy theory), applied mathematics (robotics and swarming, cryptography) and applications to magnetohydrodynamics and fluid flow.

Topology And Robotics

Author: Michael Farber
Publisher: American Mathematical Soc.
ISBN: 0821842463
Size: 21.22 MB
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Ever since the literary works of Capek and Asimov, mankind has been fascinated by the idea of robots. Modern research in robotics reveals that along with many other branches of mathematics, topology has a fundamental role to play in making these grand ideas a reality. This volume summarizes recent progress in the field of topological robotics--a new discipline at the crossroads of topology, engineering and computer science. Currently, topological robotics is developing in two main directions. On one hand, it studies pure topological problems inspired by robotics and engineering. On the other hand, it uses topological ideas, topological language, topological philosophy, and specially developed tools of algebraic topology to solve problems of engineering and computer science. Examples of research in both these directions are given by articles in this volume, which is designed to be a mixture of various interesting topics of pure mathematics and practical engineering.

Geometry Topology

Author:
Publisher:
ISBN:
Size: 38.89 MB
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Fully refereed international journal dealing with all aspects of geometry and topology and their applications.

Configuration Spaces

Author: Anders Björner
Publisher: Springer
ISBN: 8876424318
Size: 58.43 MB
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These proceedings contain the contributions of some of the participants in the "intensive research period" held at the De Giorgi Research Center in Pisa, during the period May-June 2010. The central theme of this research period was the study of configuration spaces from various points of view. This topic originated from the intersection of several classical theories: Braid groups and related topics, configurations of vectors (of great importance in Lie theory and representation theory), arrangements of hyperplanes and of subspaces, combinatorics, singularity theory. Recently, however, configuration spaces have acquired independent interest and indeed the contributions in this volume go far beyond the above subjects, making it attractive to a large audience of mathematicians.

Mod Two Homology And Cohomology

Author: Jean-Claude Hausmann
Publisher: Springer
ISBN: 3319093541
Size: 36.13 MB
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Cohomology and homology modulo 2 helps the reader grasp more readily the basics of a major tool in algebraic topology. Compared to a more general approach to (co)homology this refreshing approach has many pedagogical advantages: 1. It leads more quickly to the essentials of the subject, 2. An absence of signs and orientation considerations simplifies the theory, 3. Computations and advanced applications can be presented at an earlier stage, 4. Simple geometrical interpretations of (co)chains. Mod 2 (co)homology was developed in the first quarter of the twentieth century as an alternative to integral homology, before both became particular cases of (co)homology with arbitrary coefficients. The first chapters of this book may serve as a basis for a graduate-level introductory course to (co)homology. Simplicial and singular mod 2 (co)homology are introduced, with their products and Steenrod squares, as well as equivariant cohomology. Classical applications include Brouwer's fixed point theorem, Poincaré duality, Borsuk-Ulam theorem, Hopf invariant, Smith theory, Kervaire invariant, etc. The cohomology of flag manifolds is treated in detail (without spectral sequences), including the relationship between Stiefel-Whitney classes and Schubert calculus. More recent developments are also covered, including topological complexity, face spaces, equivariant Morse theory, conjugation spaces, polygon spaces, amongst others. Each chapter ends with exercises, with some hints and answers at the end of the book.