Labeled configuration spaces and group completions

Kazuhisa Shimakawa

Research output: Contribution to journalArticlepeer-review


Given a pair of a partial abelian monoid M and a pointed space X, let CM(ℝ, X) denote the configuration space of finite distinct points in ℝ parametrized by the partial monoid X ∧ M. In this note we will show that if M is embedded in a topological abelian group and if we put ±M = {a - b | a, b ∈ M} then the natural map CM(ℝ, X) → C ±M(ℝ, X) induced by the inclusion M ⊂ ±M is a group completion. This result can be applied to show that for any finite set M such that {0} subset of with not equal to M ⊂ ℤ, CM(ℝ, X) is weakly equivalent to the infinite loop space ΩΣX if X is connected.

Original languageEnglish
Pages (from-to)353-364
Number of pages12
JournalForum Mathematicum
Issue number2
Publication statusPublished - Mar 20 2007
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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