Geometry and Topology of Configuration Spaces

Edward R. Fadell, Sufian Y. Husseini (Autoren)

Buch | Softcover

XVI, 313 Seiten

2012 | 1. Softcover reprint of the original 1st ed. 2001
Springer Berlin (Verlag)
978-3-642-63077-4 (ISBN)

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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 Eulidean 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.

I. The Homotopy Theory of Configuration Spaces.- I. Basic Fibrations.- II. Configuration Space of ?n+1, n < 1.- III. Configuration Spaces of Sn+1, n < 1.- IV. The Two Dimensional Case.- II. Homology and Cohomology of $$(/mathbb{F}_k (M)$$.- V. The Algebra $$H^* (/mathbb{F}_k (M);/mathbb{Z})$$.- VI. Cellular Models.- VII. Cellular Chain Models.- III. Homology and Cohomology of Loop Spaces.- VIII. The Algebra $$H_* (/Omega /mathbb{F}_k (M)))$$.- IX. RPT-Constructions.- X. Cellular Chain Algebra Models.- XI. The Serre Spectral Sequence.- XII. Computation of H*(?(M)).- XIII. ?-Category and Ends.- XIV. Problems of k-body Type.- References.

Erscheint lt. Verlag	9.10.2012
Reihe/Serie	Springer Monographs in Mathematics
Zusatzinfo	XVI, 313 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	510 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	algebraic topology • cohomology • fibrations • Homology • Homotopy • homotopy theory • k-body problem • Loop group • Loop Spaces • Nonlinear analysis • Topology • Yang-Baxter equation
ISBN-10	3-642-63077-4 / 3642630774
ISBN-13	978-3-642-63077-4 / 9783642630774
Zustand	Neuware