Research

1. Coarse cohomology of the complement (with Okun), arXiv, Groups, Geometry, and Dynamics. DOI 10.4171/GGD/903

Synopsis: We define and study a notion of coarse complement of a subspace in a given metric space. We define a notion of manifold-like object in the coarse category and prove a version of coarse Alexander duality for such spaces: coarse cohomology of the complement of a subspace is determined by the coarse homology of the subspace.

2. Coarse cohomology of configuration space and coarse embedding, arXiv, Algebraic & Geometric Topology 25-7 (2025), 4391–4426.

Synopsis: We define a notion of coarse cohomology of the configuration space of a metric space X. We identify a class of degree n in that cohomology which obstructs coarse embedding of X into any uniformly contractible (n-1)-manifold.

3. On the computation of coarse cohomology, arXiv, submitted

Synopsis: We relate the coarse cohomology of a space to a more computable cohomology, called boundedly supported cohomology. As a consequence, we show that coarse cohomology of the complement (introduced in [B-Okun]) can be computed in terms of Alexander-Spanier cohomology for many spaces.

4. On the girth of groups acting on CAT(0) cube complexes (with Gulbrandsen , Mishra , and Parija) , arXiv, Algebraic & Geometric Topology 26-7 (2026), 2539-2558.

Synopsis: Every Cayley graph of an abelian group has a `small' cycle coming from the commutator relation. We prove a partial converse for CAT(0) cubulated groups: Either the group is virtually abelian, or some Cayley graphs of the group only have `large' cycles.

5. 1-Uryson width and covers (with Alpert and Papasoglu ) , arXiv , To appear in Mathematische Zeitschrift.

Synopsis: A metric space having small Uryson 1-width roughly means that the space is close to being a 1-dimensional complex. We investigate which spaces inherit this property from their universal covers: that is, we study which spaces have small Uryson 1-width when their universal covers do.

6. Cyclic orders and actions of Leary-Minasyan groups on coarse PD(n) spaces (with Schreve) , arXiv , To appear in Algebraic & Geometric Topology.

Synopsis: Cannon conjecture states that any torsion free Gromov-hyperbolic group with sphere boundary is a fundamental group of a closed 3-manifold. We present an enemy scenario to this conjecture: we show that a high dimensional generalization of this conjecture for CAT(0) groups is false.

7. Boundary dynamics, cubical actions, and infinite girth (with Amrutam , Gulbrandsen , and Mishra) , arXiv

Synopsis: We present several techniques for establishing that various classes of groups have infinite girth.

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