9 papers · 1 filter
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…
On the complexity of parametrized motion planning algorithms
Navnath Daundkar, Ekansh Jauhari
We study a probabilistic variant of the r-th sequential parametrized topological complexity, which bounds this classical invariant from below and measures the difficulty in constru…
Homotopy connectivity of Äech complexes of spheres
Henry Adams, Ekansh Jauhari, Sucharita Mallick
Let be the -sphere with the geodesic metric and of diameter . The intrinsic Äech complex of at scale is the nerve of all open balls of radius in .…
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 , , and with , we give a closed-form expression for the -th -zero-divisor cup length of the …
Bochner-type theorems for distributional category
Ekansh Jauhari, John Oprea
We show that in the presence of a geometric condition such as non-negative Ricci curvature, the distributional category of a manifold may be used to bound invariants, such as the f…
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…