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} subset of with not equal to M ⊂ ℤ, CM(ℝ∞, X) is weakly equivalent to the infinite loop space Ω∞Σ∞X if X is connected.
Original language | English |
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Pages (from-to) | 353-364 |
Number of pages | 12 |
Journal | Forum Mathematicum |
Volume | 19 |
Issue number | 2 |
DOIs | |
Publication status | Published - Mar 20 2007 |
Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics