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Labeled configuration spaces and group completions
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Kazuhisa Shimakawa
Veröffentlicht/Copyright:
12. März 2007
Abstract
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} ⊊ M ⊂ ℤ, CM(ℝ∞, X) is weakly equivalent to the infinite loop space Ω∞Σ∞X if X is connected.
Received: 2003-05-16
Revised: 2005-07-02
Revised: 2006-03-20
Published Online: 2007-03-12
Published in Print: 2007-03-20
© Walter de Gruyter
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Artikel in diesem Heft
- P-adic logarithmic forms and group varieties III
- Moving homology classes to infinity
- On a class of locally finite T-groups
- On Ext-universal modules in Gödel's universe
- Paraproducts in one and several parameters
- Labeled configuration spaces and group completions
- Universal localizations embedded in power-series rings
Artikel in diesem Heft
- P-adic logarithmic forms and group varieties III
- Moving homology classes to infinity
- On a class of locally finite T-groups
- On Ext-universal modules in Gödel's universe
- Paraproducts in one and several parameters
- Labeled configuration spaces and group completions
- Universal localizations embedded in power-series rings
