Ekansh Jauhari

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math.AT2026

Homotopic distances and group-like spaces

Ekansh Jauhari, John Oprea

Homotopic distance is a numerical homotopy invariant that quantifies the homotopic distinction between two or more continuous maps. In this paper, we look at various versions of ho…

math.AT2026

On the sequential topological complexity and the LS-category of the cofiber of higher diagonals for symmetric products of non-orientable surfaces

Jesús González, Ekansh Jauhari

For positive integers $k$ , $n$ , and $g$ with $k \geq 2$ , we give a closed-form expression for the $k$ -th $Z_{2}$ -zero-divisor cup length $zcl_{k} (S P^{n} (N_{g}))$ of the $n$ …

math.AT2025

On distributional one-category, diagonal distributional complexity, and related invariants

Ekansh Jauhari, John Oprea

We develop the theory of probabilistic variants of the one-category and diagonal topological complexity, which bound the classical LS-category and topological complexity from below…

math.AT2025

LS-category and sequential topological complexity of symmetric products

Ekansh Jauhari

The $n$ -th symmetric product of a topological space $X$ is the orbit space of the natural action of the symmetric group $S_{n}$ on the product space $X^{n}$ . In this paper, we compute…

math.AT2025

Homotopy connectivity of Čech complexes of spheres

Henry Adams, Ekansh Jauhari, Sucharita Mallick

Let $S^{n}$ be the $n$ -sphere with the geodesic metric and of diameter $π$ . The intrinsic Čech complex of $S^{n}$ at scale $r$ is the nerve of all open balls of radius $r$ in $S^{n}$ . In…