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Configuration spaces with summable labels

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Part of the Progress in Mathematics book series (PM,volume 196)

Abstract

An n-monoid is the appropriate extension of an A -space for the theory of n-fold loop spaces. We define spaces of configurations on n-manifolds with summable labels in partial n-monoids. In particular we obtain an n-fold delooping machinery, that extends the construction of the classifying space by Stasheff. Our configuration spaces cover also symmetric products, spaces of rational curves and spaces of labelled subsets. A configuration space with connected space of labels has the homotopy type of the space of sections of a certain bundle. This extends and unifies results by Bödigheimer, Guest, Kallel and May.

Keywords

  • Configuration Space
  • Homotopy Type
  • Rational Curf
  • Internal Edge
  • Forgetful Functor

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 Basel AG

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Salvatore, P. (2001). Configuration spaces with summable labels. In: Aguadé, J., Broto, C., Casacuberta, C. (eds) Cohomological Methods in Homotopy Theory. Progress in Mathematics, vol 196. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8312-2_23

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  • DOI: https://doi.org/10.1007/978-3-0348-8312-2_23

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9513-2

  • Online ISBN: 978-3-0348-8312-2

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