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Using the Borsuk-Ulam Theorem / Lectures on Topological Methods in Combinatorics and Geometry, Matousek Jiri, Björner A., Ziegler G.M.

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: Matousek Jiri, Björner A., Ziegler G.M.
 Using the Borsuk-Ulam Theorem / Lectures on Topological Methods in Combinatorics and Geometry
:  -
ISBN: 9783540003625
: Springer

ISBN-10: 3540003622
/: Paperback
: 226
: 0.398 .
: 01.04.2003
: Universitext
: English
: Softcover reprint of
: Bibliography, index
: 232 x 158 x 14
: Postgraduate, research & scholarly
: Lectures on topological methods in combinatorics and geometry
: Link
: : 235x155
:  Researchers, graduate and undergraduate students in Combinatorics and Combinatorial Geometry,  Algebraic Topology and  Theoretical Computer Science
: Combinatorics
applications of algebraic topology
discrete geometry
: eng
: Preliminaries.- 1 Simplicial Complexes: 1.1 Topological spaces; 1.2 Homotopy equivalence and homotopy; 1.3 Geometric simplicial complexes; 1.4 Triangulations; 1.5 Abstract simplicial complexes; 1.6 Dimension of geometric realizations; 1.7 Simplicial complexes and posets.- 2 The Borsuk-Ulam Theorem: 2.1 The Borsuk-Ulam theorem in various guises; 2.2 A geometric proof; 2.3 A discrete version: Tucker's lemma; 2.4 Another proof of Tucker's lemma.- 3 Direct Applications of Borsuk--Ulam: 3.1 The ham sandwich theorem; 3.2 On multicolored partitions and necklaces; 3.3 Kneser's conjecture; 3.4 More general Kneser graphs: Dolnikov's theorem; 3.5 Gale's lemma and Schrijver's theorem.- 4 A Topological Interlude: 4.1 Quotient spaces; 4.2 Joins (and products); 4.3 k-connectedness; 4.4 Recipes for showing k-connectedness; 4.5 Cell complexes.- 5 Z_2-Maps and Nonembeddability: 5.1 Nonembeddability theorems: An introduction; 5.2 Z_2-spaces and Z_2-maps; 5.3 The Z_2-index; 5.4 Deleted products good ...; 5.5 ... deleted joins better; 5.6 Bier spheres and the Van Kampen-Flores theorem; 5.7 Sarkaria's inequality; 5.8 Nonembeddability and Kneser colorings; 5.9 A general lower bound for the chromatic number.- 6 Multiple Points of Coincidence: 6.1 G-spaces; 6.2 E_nG spaces and the G-index; 6.3 Deleted joins and deleted products; 6.4 Necklace for many thieves; 6.5 The topological Tverberg theorem; 6.6 Many Tverberg partitions; 6.7 Z_p-index, Kneser colorings, and p-fold points; 6.8 The colored Tverberg theorem.- A Quick Summary.- Hints to Selected Exercises.- Bibliography.- Index.

Combinatorics, Geometry and Probability

: Edited by B?la Bollob?s
: Combinatorics, Geometry and Probability
ISBN: 0521607663 ISBN-13(EAN): 9780521607667
: Cambridge Academ
: 8314 .
  : .

: Paul Erdos was one of the greatest mathematicians of this century, known the world over for his brilliant ideas and stimulating questions. On the date of his 80th birthday a conference was held in his honour at Trinity College, Cambridge. Many leading combinatorialists attended. Their subsequent contributions are collected here. The areas represented range from set theory and geometry, through graph theory, group theory and combinatorial probability, to randomised algorithms and statistical physics. Erdos himself was able to give a survey of recent progress made on his favourite problems. Consequently this volume, consisting of in-depth studies at the frontier of research, provides a valuable panorama across the breadth of combinatorics as it is today.

Algebraic Combinatorics / Lectures at a Summer School in Nordfjordeid, Norway, June 2003

: Orlik Peter, Welker Volkmar, Floystad Gunnar
: Algebraic Combinatorics / Lectures at a Summer School in Nordfjordeid, Norway, June 2003
ISBN: 3540683755 ISBN-13(EAN): 9783540683759
: Springer
: 8160 .
  : .

: This book is based on two series of lectures given at a summer school on algebraic combinatorics at the Sophus Lie Centre in Nordfjordeid, Norway, in June 2003, one by Peter Orlik on hyperplane arrangements, and the other one by Volkmar Welker on free resolutions. Both topics are essential parts of current research in a variety of mathematical fields, and the present book makes these sophisticated tools available for graduate students.

Lectures on topological fluid mechanics

: Berger, Mitchell A. Kauffman, Louis H. Khesin, Bor
: Lectures on topological fluid mechanics
ISBN: 3642008364 ISBN-13(EAN): 9783642008368
: Springer
: 7418 .
  : .

: Contains research papers that cover topics such as fundamental aspects of mathematical fluid mechanics, topological vortex dynamics and magnetohydrodynamics, integrability issues, Hamiltonian structures and singularity formation, DNA tangles and knotted DNAs in sedimentation.

Geometric, Algebraic and Topological Methods for Quantum Fie

: Cardona Alexander
: Geometric, Algebraic and Topological Methods for Quantum Fie
ISBN: 9814460044 ISBN-13(EAN): 9789814460040
: World Scientific Publishing
: 24224 .
  : .

: Based on lectures held at the 7th Villa de Leyva summer school, this book presents an introduction to topics of current interest in the interface of geometry, topology and physics. It is aimed at graduate students in physics or mathematics with interests in geometric, algebraic as well as topological methods and their applications to quantum field theory.This volume contains the written notes corresponding to lectures given by experts in the field. They cover current topics of research in a way that is suitable for graduate students of mathematics or physics interested in the recent developments and interactions between geometry, topology and physics. The book also contains contributions by younger participants, displaying the ample range of topics treated in the school. A key feature of the present volume is the provision of a pedagogical presentation of rather advanced topics, in a way which is suitable for both mathematicians and physicists.

User`s approach for topological methods in 3d dynamical systems, the

: User`s approach for topological methods in 3d dynamical systems, the
ISBN: 9812703802 ISBN-13(EAN): 9789812703804
: World Scientific Publishing
: 14823 .
  : .

: This book presents the development and application of some topological methods in the analysis of data coming from 3D dynamical systems (or related objects). The aim is to emphasize the scope and limitations of the methods, what they provide and what they do not provide. Braid theory, the topology of surface homeomorphisms, data analysis and the reconstruction of phase-space dynamics are thoroughly addressed.

Geometric and Topological Methods for Quantum Field Theory

: Ocampo Hernan, Paycha Sylvie, Vargas Andrés
: Geometric and Topological Methods for Quantum Field Theory
ISBN: 354024283X ISBN-13(EAN): 9783540242833
: Springer
: 18041 .
  : .

: This volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is by Christine Lescop on knot invariants and configuration spaces, in which a universal finite-type invariant for knots is constructed as a series of integrals over configuration spaces. This is followed by the contribution of Raimar Wulkenhaar on Euclidean quantum field theory from a statistical point of view. The author also discusses possible renormalization techniques on noncommutative spaces. The third lecture is by Anamaria Font and Stefan Theisen on string compactification with unbroken supersymmetry. The authors show that this requirement leads to internal spaces of special holonomy and describe Calabi-Yau manifolds in detail. The last lecture, by Thierry Fack, is devoted to a K-theory proof of the Atiyah-Singer index theorem and discusses some applications of K-theory to noncommutative geometry. These lectures notes, which are aimed in particular at graduate students in physics and mathematics, start with introductory material before presenting more advanced results. Each chapter is self-contained and can be read independently.

Topological Methods in Hydrodynamics

: Arnold
: Topological Methods in Hydrodynamics
ISBN: 038794947X ISBN-13(EAN): 9780387949475
: Springer
: 19304 .
  : .

: Topological hydrodynamics is a young branch of mathematics studying topological features of flows with complicated trajectories, as well as their applications to fluid motions. It is situated at the crossroad of hyrdodynamical stability theory, Riemannian and symplectic geometry, magnetohydrodynamics, theory of Lie algebras and Lie groups, knot theory, and dynamical systems. Applications of this approach include topological classification of steady fluid flows, descriptions of the Korteweg-de Vries equation as a geodesic flow, and results on Riemannian geometry of diffeomorphism groups, explaining, in particular, why longterm dynamical weather forecasts are not reliable.

Topological Methods in Hydrodynamics is the first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics for a unified point of view. T e necessary preliminary notions both in hydrodynamics and pure mathematics are described with plenty of examples and figures. The book is accessible to graduate students as well as to both pure and applied mathematicians working in the fields of hydrodynamics, Lie groups, dynamical systems and differential geometry.

Groups, combinatorics and geometry

: Groups, combinatorics and geometry
ISBN: 9812383123 ISBN-13(EAN): 9789812383129
: World Scientific Publishing
: 16089 .
  : .

: Since the 1980s, the theory of groups - in particular simple groups, finite and algebraic - has influenced a number of diverse areas of mathematics. Such areas include topics where groups have been traditionally applied, such as algebraic combinatorics, finite geometries, Galois theory and permutation groups, as well as several more recent developments. Among the latter are probabilistic and computational group theory, the theory of algebraic groups over number fields, and model theory, in each of which th re has been a major recent impetus provided by simple group theory.

In addition, there is still great interest in local analysis in finite groups, with substantial new input from methods of geometry and amalgams, and particular emphasis on the revision project for the classification of finite simple groups. This book contains 20 survey articles covering many of the above developments. It should prove valuable for those working in the theory of groups and its applications.

Lectures on advances in combinatorics

: Ahlswede, Rudolf Blinovsky, Vladimir
: Lectures on advances in combinatorics
ISBN: 3540786015 ISBN-13(EAN): 9783540786016
: Springer
: 7424 .
  : .

: Includes a solution to the 4m-conjecture of Erdos/Ko/Rado 1938, an answer to a question of Erdos (1962) in combinatorial number theory, and the discovery that the AD-inequality implies more general and sharper number theoretical inequalities than for instance Behrend`s inequality.

Discrete Geometry, Combinatorics and Graph Theory

: Jin Akiyama; William Y.C. Chen; Mikio Kano; Xuelia
: Discrete Geometry, Combinatorics and Graph Theory
ISBN: 3540706658 ISBN-13(EAN): 9783540706656
: Springer
: 10394 .
  : .

: This book constitutes the thoroughly refereed post-proceedings of the 7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005, held in Tianjin, China, as well as in Xi`an, China, in November 2005. The 30 revised full papers address all current issues in discrete algorithmic geometry, combinatorics and graph theory.

Topological methods for set-valued nonlinear analysis

: Topological methods for set-valued nonlinear analysis
ISBN: 9812704671 ISBN-13(EAN): 9789812704672
: World Scientific Publishing
: 29466 .
  : .

: This book provides a comprehensive overview of the authors' pioneering contributions to nonlinear set-valued analysis by topological methods. The coverage includes fixed point theory, degree theory, the KKM principle, variational inequality theory, the Nash equilibrium point in mathematical economics, the Pareto optimum in optimization, and applications to best approximation theory, partial equations and boundary value problems. Self-contained and unified in presentation, the book considers the existence of equilibrium points of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities.

It also provides the latest developments in KKM theory and degree theory for nonlinear set-valued mappings.

Topological methods, variational methods and their applications - proceedings of the icm2002 satellite conference on nonlinear functional analysis

: Topological methods, variational methods and their applications - proceedings of the icm2002 satellite conference on nonlinear functional analysis
ISBN: 9812382623 ISBN-13(EAN): 9789812382627
: World Scientific Publishing
: 16089 .
  : .

: ICM 2002 Satellite Conference on Nonlinear Analysis was held in the period: August 14 18, 2002 at Taiyuan, Shanxi Province, China. This conference was organized by Mathematical School of Peking University, Academy of Ma hematics and System Sciences of Chinese Academy of Sciences, Mathematical school of Nankai University, and Department of Mathematics of Shanxi University, and was sponsored by Shanxi Province Education Committee, Tian Yuan Mathematics Foundation, and Shanxi University. Attending the conference were 166 mathematicians from 21 countries and areas in the world with 53 invited speakers and 30 contributors presenting their lectures.

This conference aims at an overview of the recent development in nonlinear analysis. It covers the following topics: variational methods, topological methods, fixed point theory, bifurcations, nonlinear spectral theory, nonlinear Schrodinger equations, semilinear elliptic equations, Hamiltonian systems, central configuration in N-body problems and variational problems arising in geometry and physics.

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