2 results
Continuum of allosteric actions for non-amenable surface groups
- Part of
-
- Journal:
- Ergodic Theory and Dynamical Systems / Volume 44 / Issue 6 / June 2024
- Published online by Cambridge University Press:
- 19 July 2023, pp. 1581-1596
- Print publication:
- June 2024
-
- Article
-
- You have access
- HTML
- Export citation
-
Let
$\Sigma $ be a closed surface other than the sphere, the torus, the projective plane or the Klein bottle. We construct a continuum of probability measure preserving ergodic minimal profinite actions for the fundamental group of 
$\Sigma $ that are topologically free but not essentially free, a property that we call allostery. Moreover, the invariant random subgroups we obtain are pairwise distincts.
On the Balmer spectrum for compact Lie groups
- Part of
-
- Journal:
- Compositio Mathematica / Volume 156 / Issue 1 / January 2020
- Published online by Cambridge University Press:
- 14 November 2019, pp. 39-76
- Print publication:
- January 2020
-
- Article
- Export citation
-
We study the Balmer spectrum of the category of finite
$G$-spectra for a compact Lie group 
$G$, extending the work for finite 
$G$ by Strickland, Balmer–Sanders, Barthel–Hausmann–Naumann–Nikolaus–Noel–Stapleton and others. We give a description of the underlying set of the spectrum and show that the Balmer topology is completely determined by the inclusions between the prime ideals and the topology on the space of closed subgroups of 
$G$. Using this, we obtain a complete description of this topology for all abelian compact Lie groups and consequently a complete classification of thick tensor ideals. For general compact Lie groups we obtain such a classification away from a finite set of primes 
$p$.
