2 results
FINITE-DIMENSIONAL ORDERED VECTOR SPACES WITH RIESZ INTERPOLATION AND EFFROS–SHEN’S UNIMODULARITY CONJECTURE
- Part of
-
- Journal:
- Journal of the Australian Mathematical Society / Volume 101 / Issue 2 / October 2016
- Published online by Cambridge University Press:
- 13 May 2016, pp. 277-287
- Print publication:
- October 2016
-
- Article
-
- You have access
- Export citation
-
It is shown that, for any field
$\mathbb{F}\subseteq \mathbb{R}$, any ordered vector space structure of 
$\mathbb{F}^{n}$ with Riesz interpolation is given by an inductive limit of a sequence with finite stages 
$(\mathbb{F}^{n},\mathbb{F}_{\geq 0}^{n})$ (where 
$n$ does not change). This relates to a conjecture of Effros and Shen, since disproven, which is given by the same statement, except with 
$\mathbb{F}$ replaced by the integers, 
$\mathbb{Z}$. Indeed, it shows that although Effros and Shen’s conjecture is false, it is true after tensoring with 
$\mathbb{Q}$.
AN EXPLICIT DESCRIPTION OF THE SIMPLICIAL GROUP
$K(A, n)$
- Part of
-
- Journal:
- Journal of the Australian Mathematical Society / Volume 95 / Issue 1 / August 2013
- Published online by Cambridge University Press:
- 07 June 2013, pp. 133-144
- Print publication:
- August 2013
-
- Article
-
- You have access
- Export citation
-
We give an explicit construction for a
$K(A, n)$ simplicial group and explain its topological interpretation.
