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Geometry And Topology Of Configuration Spaces (springer Monographs In Mathematics) 🔍
Edward R. Fadell, Sufian Y. Husseini (auth.) Springer-Verlag Berlin Heidelberg, Springer Monographs in Mathematics, Springer Monographs in Mathematics, 1, 2001
English [en] · PDF · 11.6MB · 2001 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/scihub/zlib · Save
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 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.
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lgrsnf/A:\compressed\10.1007%2F978-3-642-56446-8.pdf
Alternative filename
nexusstc/Geometry and Topology of Configuration Spaces/7393aeeafcff23433665bf6fe0d60396.pdf
Alternative filename
scihub/10.1007/978-3-642-56446-8.pdf
Alternative author
by Edward R. Fadell, Sufian Y. Husseini
Alternative author
Fadell, Edward R., Husseini, Sufian Y.
Alternative publisher
Spektrum Akademischer Verlag. in Springer-Verlag GmbH
Alternative publisher
Springer Berlin Heidelberg : Imprint : Springer
Alternative publisher
Steinkopff. in Springer-Verlag GmbH
Alternative edition
Springer Monographs in Mathematics, Springer monographs in mathematics, Berlin, Heidelberg, Germany, 2001
Alternative edition
Springer Nature, Berlin, Heidelberg, 2012
Alternative edition
Germany, Germany
Alternative edition
1, US, 2012
Alternative edition
1, 2013
metadata comments
lg951238
metadata comments
{"container_title":"Springer Monographs in Mathematics","edition":"1","isbns":["3642564461","3642630774","9783642564468","9783642630774"],"issns":["1439-7382"],"last_page":313,"publisher":"Springer","series":"Springer Monographs in Mathematics"}
metadata comments
Online full text is restricted to subscribers.
Also available in print.
Mode of access: World Wide Web.
Alternative description
Front Matter....Pages i-xvi
Front Matter....Pages 1-1
Introduction....Pages 3-4
Basic Fibrations....Pages 5-12
Configuration Space of R n+1 , n > 1....Pages 13-28
Configuration Spaces of S n+1 , n > 1....Pages 29-55
The Two Dimensional Case....Pages 57-90
Front Matter....Pages 91-91
Introduction....Pages 93-94
The Algebra H *( $$ {\Bbb F}$$ k ( M );Z)....Pages 95-115
Cellular Models....Pages 117-151
Cellular Chain Models....Pages 153-163
Front Matter....Pages 165-165
Introduction....Pages 167-169
The Algebra H * (Ω $$ {\Bbb F}$$ k ( M )))....Pages 171-185
RPT-Constructions....Pages 187-206
Cellular Chain Algebra Models....Pages 207-223
The Serre Spectral Sequence....Pages 225-242
Computation of H * ( Λ ( M ))....Pages 243-267
Γ -Category and Ends....Pages 269-291
Problems of k -body Type....Pages 293-303
Back Matter....Pages 305-313
Alternative description
Part 1: The Homotopy of Configuration Spaces. Basic Fibrations. Configuration space of Euclidean Space. Configuration spaces on spheres. The two-dimensional case
Part 2: The cohomology algebra of configuration spaces. Cellular models. Cellular chain models
Part 3: The Homology of Based Loops. RPT-Constructions. Cellular chain algebra models. The Serre spectral sequence. Computation of the homology of the free loop space. Ends and Gamma category. An application to problems of k-body type.
Alternative description
<p>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.</p>
Alternative description
Springer Monographs in Mathematics
Erscheinungsdatum: 09.10.2012
date open sourced
2013-08-01
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