Zobrazeno 1 - 10
of 28
pro vyhledávání: '"Allison, Shaun"'
For each ordinal $\alpha<\omega_1$, we introduce the class of $\alpha$-balanced Polish groups. These classes form a hierarchy that completely stratifies the space between the class of Polish groups admitting a two-side-invariant metric (TSI) and the
Externí odkaz:
http://arxiv.org/abs/2406.06082
Autor:
Allison, Shaun
Gao and Jackson showed that any countable Borel equivalence relation (CBER) induced by a countable abelian Polish group is hyperfinite. This prompted Hjorth to ask if this is in fact true for all CBERs classifiable by (uncountable) abelian Polish gro
Externí odkaz:
http://arxiv.org/abs/2305.01049
Autor:
Allison, Shaun
In recent years, much work has been done to measure and compare the complexity of orbit equivalence relations, especially for certain classes of Polish groups. We start by introducing some language to organize this previous work, namely the notion of
Externí odkaz:
http://arxiv.org/abs/2304.00139
Autor:
Allison, Shaun, Shani, Assaf
A Polish group $G$ is tame if for any continuous action of $G$, the corresponding orbit equivalence relation is Borel. When $G = \prod_n \Gamma_n$ for countable abelian $\Gamma_n$, Solecki (1995) gave a characterization for when $G$ is tame. Ding and
Externí odkaz:
http://arxiv.org/abs/2105.05144
Autor:
Allison, Shaun
A variation of the Scott analysis of countable structures is applied to actions of non-Archimedean TSI Polish groups acting continuously on a Polish spaces. We give results on the potential Borel complexity spectrum of such groups, and define orbit e
Externí odkaz:
http://arxiv.org/abs/2010.05085
In the spirit of Hjorth's turbulence theory, we introduce "unbalancedness": a new dynamical obstruction to classifying orbit equivalence relations by actions of Polish groups which admit a two side invariant metric (TSI). Since abelian groups are TSI
Externí odkaz:
http://arxiv.org/abs/2004.07409