7 papers
The class and dynamics of -balanced Polish groups
Shaun Allison, Aristotelis Panagiotopoulos
For each ordinal , we introduce the class of -balanced Polish groups. These classes form a hierarchy that completely stratifies the space between the class of Polish g…
The definable content of homological invariants I: &
Jeffrey Bergfalk, Martino Lupini, Aristotelis Panagiotopoulos
This is the first installment in a series of papers in which we illustrate how classical invariants of homological algebra and algebraic topology can be enriched with additional de…
Quasi-invariant measures concentrating on countable structures
Clinton Conley, Colin Jahel, Aristotelis Panagiotopoulos
Countable -structures whose isomorphism class supports a permutation invariant probability measure in the logic action have been characterized by Ackerma…
The definable content of homological invariants II: Äech cohomology and homotopy classification
Jeffrey Bergfalk, Martino Lupini, Aristotelis Panagiotopoulos
This is the second installment in a series of papers applying descriptive set theoretic techniques to both analyze and enrich classical functors from homological algebra and algebr…
Definable (co)homology, pro-torus rigidity, and (co)homological classification
Jeffrey Bergfalk, Martino Lupini, Aristotelis Panagiotopoulos
We show that the classical homology theory of Steenrod may be enriched with descriptive set-theoretic information. We prove that the resulting definable homology theory provides a…
Strong ergodicity phenomena for Bernoulli shifts of bounded algebraic dimension
Aristotelis Panagiotopoulos, Assaf Shani
The algebraic dimension of a Polish permutation group is the smallest , so that for all of size , the orbit of…