SOME REMARKS ON CONFIGURATION SPACES

Autor(en): Raptis, George
Stichwörter: CELL-LIKE MAPPINGS; cell-like maps; Configuration spaces; MANIFOLDS; Mathematics; Mathematics, Applied
Erscheinungsdatum: 2011
Herausgeber: AMER MATHEMATICAL SOC
Journal: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volumen: 139
Ausgabe: 5
Startseite: 1879
Seitenende: 1887
Zusammenfassung: 
This paper studies the homotopy type of the configuration spaces F-n(X) by introducing the idea of configuration spaces of maps. For every map f : X -> Y, the configuration space F-n(f) is the space of configurations in X that have distinct images in Y. We show that the natural maps F-n(X) <- F-n(f) -> F-n(Y) are homotopy equivalences when f is a proper cell-like map between d-manifolds. We also show that the best approximation to X bar right arrow F-n(X) by a homotopy invariant functor is given by the n-fold product map.
ISSN: 00029939
DOI: 10.1090/S0002-9939-2010-10580-4

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