Irakli Patchkoria

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20232025

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math.AT2025

On the Farrell--Tate $K$ -theory of $Out (F_{n})$

Naomi Andrew, Irakli Patchkoria

Using Lück's Chern character isomorphism we obtain a general formula in terms of centralisers for the $p$ -adic Farrell--Tate $K$ -theory of any discrete group $G$ with a finite clas…

math.AT2024

Chromatic congruences and Bernoulli numbers

Irakli Patchkoria

For every natural number $n$ and a fixed prime $p$ , we prove a new congruence for the orbifold Euler characteristic of a group. The $p$ -adic limit of these congruences as $n$ tends…

math.AT2023

On the cyclic homology of certain universal differential graded algebras

Christopher Davis, Julius Frank, Irakli Patchkoria

Let $p$ be an odd prime and $R$ a $p$ -torsion-free commutative $Z_{(p)}$ -algebra. We compute the periodic cyclic homology over $R$ of the universal differential graded alg…

On the Farrell--Tate K-theory of Out(Fn​)

Chromatic congruences and Bernoulli numbers

On the cyclic homology of certain universal differential graded algebras

On the Farrell--Tate $K$ -theory of $Out (F_{n})$