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• catalog abstract ""The configuration space of a manifold provides the appropriate setting for problems not only in topology but also in other areas such as nonlinear analysis and algebra. With applications in mind, the aim of this monograph is to provide a coherent and thorough treatment of the configuration spaces of Euclidean spaces and spheres which makes the subject accessible to researchers and graduate students with a minimal background in classical homotopy theory and algebraic topology. The treatment regards the homotopy relations of Yang-Baxter type as being fundamental. It also includes a novel and geometric presentation of the classical pure braid group; the cellular structure of these configuration spaces which leads to a cellular model for the associated based and free loop spaces; the homology and cohomology of based and free loop spaces; and an illustration of how to apply the latter to the study of Hamiltonian systems of k-body type."--Jacket.".
• catalog contributor b12042789.
• catalog contributor b12042790.
• catalog created "c2001.".
• catalog date "2001".
• catalog date "c2001.".
• catalog dateCopyrighted "c2001.".
• catalog description ""The configuration space of a manifold provides the appropriate setting for problems not only in topology but also in other areas such as nonlinear analysis and algebra. With applications in mind, the aim of this monograph is to provide a coherent and thorough treatment of the configuration spaces of Euclidean spaces and spheres which makes the subject accessible to researchers and graduate students with a minimal background in classical homotopy theory and algebraic topology. The treatment regards the homotopy relations of Yang-Baxter type as being fundamental. It also includes a novel and geometric presentation of the classical pure braid group; the cellular structure of these configuration spaces which leads to a cellular model for the associated based and free loop spaces; the homology and cohomology of based and free loop spaces; and an illustration of how to apply the latter to the study of Hamiltonian systems of k-body type."--Jacket.".
• catalog description "Includes bibliographical references (p. [305]-309) and index.".
• catalog description "Pt. I. The Homotopy Theory of Configuration Spaces -- I. Basic Fibrations -- II. Configuration Space of R[superscript n+1], n > 1 -- III. Configuration Spaces of S[superscript n+1], n > 1 -- IV. The Two Dimensional Case -- Pt. II. Homology and Cohomology of F[subscript k](M) -- V. The Algebra H (F[subscript k](M);Z) -- VI. Cellular Models -- VII. Cellular Chain Models -- Pt. III. Homology and Cohomology of Loop Spaces -- VIII. The Algebra H ([Omega]F[subscript k](M))) -- IX. RPT-Constructions -- X. Cellular Chain Algebra Models -- XI. The Serre Spectral Sequences -- XII. Computation of H ([Lambda](M)) -- XIII. [Gamma]-Category and Ends -- XIV. Problems of k-body Type.".
• catalog extent "xvi, 313 p. :".
• catalog identifier "3540666699 (alk. paper)".
• catalog isPartOf "Springer monographs in mathematics, 1439-7382".
• catalog issued "2001".
• catalog issued "c2001.".
• catalog language "eng".
• catalog publisher "Berlin ; New York : Springer,".
• catalog subject "516.3/5 21".
• catalog subject "Algebraic topology.".
• catalog subject "Configuration space.".
• catalog subject "QA607 .F34 2001".
• catalog tableOfContents "Pt. I. The Homotopy Theory of Configuration Spaces -- I. Basic Fibrations -- II. Configuration Space of R[superscript n+1], n > 1 -- III. Configuration Spaces of S[superscript n+1], n > 1 -- IV. The Two Dimensional Case -- Pt. II. Homology and Cohomology of F[subscript k](M) -- V. The Algebra H (F[subscript k](M);Z) -- VI. Cellular Models -- VII. Cellular Chain Models -- Pt. III. Homology and Cohomology of Loop Spaces -- VIII. The Algebra H ([Omega]F[subscript k](M))) -- IX. RPT-Constructions -- X. Cellular Chain Algebra Models -- XI. The Serre Spectral Sequences -- XII. Computation of H ([Lambda](M)) -- XIII. [Gamma]-Category and Ends -- XIV. Problems of k-body Type.".
• catalog title "Geometry and topology of configuration spaces / Edward R. Fadell, Sufian Y. Husseini.".
• catalog type "text".