Geometry and Topology of Configuration Spaces

2001
ISBN: 978-3-540-66669-1
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 313 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1430 g

Reihe: Springer Monographs in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Husseini, Sufian Y.

Fadell, Edward R.

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Geometrie Euklidische Geometrie

Inhaltsverzeichnis

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.