Harsh Patil

collaborators

4 papers

math.MG2026

A Finitary Approach to Coarse Separation of Euclidean spaces

Harsh Patil

We give a novel proof of the fact that every coarsely separating family of subsets of the Euclidean space $R^{d}$ must have asymptotic dimension at least $d - 1$ . The proof…

math.GR2025

Finiteness properties and Relatively Hyperbolic Groups

Harsh Patil

We show that properties $F_{n}$ and $F P_{n}$ hold for a relatively hyperbolic group if and only if they hold for all the peripheral subgroups. As an application we show that there are…

math.GR2025

Relative cohomological dimension of a relatively hyperbolic pair

Harsh Patil

We show that the relative cohomological dimension $\cd(G,H)$ of a relatively hyperbolic pair $(G, H)$ is always finite when $G$ is torsion-free. We also show that this dimension is…

math.GT2025

Generating the liftable mapping class groups of regular cyclic covers

Soumya Dey, Neeraj K. Dhanwani, Harsh Patil +1

Let $Mod (S_{g})$ be the mapping class group of the closed orientable surface of genus $g \geq 1$ , and let $LMod_{p} (X)$ be the liftable mapping class group associat…