arXiv subjects

Kostyantyn Krutoy

Publications and source records attributed to Kostyantyn Krutoy.

2 recordsLinked to original sources

arXiv2026

Bijective rigidity of uniform Roe algebras and injectivity of the comparison map

We show that, for uniformly locally finite metric spaces $X$ and $Y$ with isomorphic uniform Roe algebras $C^*_u(X)$ and $C^*_u(Y)$, the existence of a bijective coarse equivalence $f \colon X \to Y$ is equivalent to the injectivity of the $0$th comparison map appearing in the HK conjecture for coarse groupoids. We further prove that the $0$th comparison map is injective unconditionally. Moreover, if the underlying space is coarsely connected, this map is in fact split-injective.

math.OA↗

arXiv2025

Categorical approach to rigidity of Roe-like algebras of coarse spaces

We demonstrate that any full and faithful $*$-functor between approximable categories of locally finite coarse spaces induces a coarse embedding between the underlying spaces. Furthermore, we establish a general characterisation of such $*$-functors between approximable categories and prove that the functor associating each locally finite coarse space with its approximable category is full and faithful.

math.OA↗