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RPT-Constructions

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Abstract

Our aim in this chapter is to represent the spaces of based and free loops Ω(X) and Λ(X) as well as other associated spaces of a simply connected, countable CW-complex X with a single 0-vertex, e, as CW-complexes of a certain kind. In the case of Ω(X), the complex will have a nondegenerate product corresponding to the usual path multiplication. The first example of such constructions is the reduced-product complex X of [63, James]. The complexes we construct generalize his construction and will be called constructions of the reduced-product type, or RPT-complexes for short.

Keywords

  • Spectral Sequence
  • Homotopy Group
  • Special Complex
  • Homotopy Equivalence
  • Serre Spectral Sequence

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2001 Springer-Verlag Berlin Heidelberg

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Fadell, E.R., Husseini, S.Y. (2001). RPT-Constructions. In: Geometry and Topology of Configuration Spaces. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56446-8_12

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  • DOI: https://doi.org/10.1007/978-3-642-56446-8_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-63077-4

  • Online ISBN: 978-3-642-56446-8

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