Rakesh Halder

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math.GT2026

Finiteness of Cannon--Thurston fibers

Indranil Bhattacharyya, Rakesh Halder, Nir Lazarovich +1

Let $Y \to X$ be a proper map between proper hyperbolic metric spaces. A Cannon--Thurston map is a continuous extension $\partial Y \to \partial X$ . We prove that in most known sett…

math.GT2026

Embeddings of trees of hyperbolic metric spaces and Cannon--Thurston maps

Rakesh Halder, Pranab Sardar

Given a tree of hyperbolic metric spaces $I ¨ : X \to T$ a la Bestvina--Feighn (\cite{BF}), and a hyperbolic subspace $Y$ of $X$ with an induced tree of hyperbolic spaces structure ove…

math.GT2025

Surjectivity of the Cannon--Thurston map in metric (graph) bundles

Rakesh Halder

Metric (graph) bundles generalize the notion of fiber bundles to the context of geometric group theory and were introduced by Mj and Sardar. Suppose $X$ is a metric (graph) bundle…

math.GT2025

Landing rays and ray Cannon-Thurston maps

Rakesh Halder, Mahan Mj, Pranab Sardar

In this paper, we describe a procedure to construct pairs of hyperbolic groups $H < G$ with the following properties. 1) Every geodesic ray $I^^{3}$ in $H$ converges to a point $Î¾_Î³\in…