Yuli B. Rudyak

activity

19972024

most citedOn the Berstein-Svarc Theorem in dimension 2

45 citations · 175 across the 43 of their papers we have counts for

collaborators

44 papers

math.AT2024

On spaces of minimal higher topological complexity

Yuli Rudyak

Let TC $_{n}$ (X) denote the n-th topological complexity of a topological space X. It is known that TC $_{n}$ (X) does not exceed n-1 for non-contractible X, and so it makes sense to descr…

math.GT2023

Maps of Degree One, Lusternik Schnirelmann Category, and Critical Points

Deep Kundu, Yuli B. Rudyak

Let $C r i tM$ denote the minimal number of critical points (not necessarily non-degenerate) on a closed smooth manifold $M$ . We are interested in the evaluation of $C r i t$ . It is wor…

math.GM2022

A Variant of Probabilistic Topology

Yuli B. Rudyak

Here I discuss ideas that makes a synthesis of topology and probability theory. The idea is the following: given a set $X$ , assign a number $p (A) \in [0, 1]$ for any subset $A$ of $X…

math.AT2021

Relative LS categories and higher topological complexities of maps

Yuli B. Rudyak, Soumen Sarkar

In this paper, we study three relative LS categories of a map and study some of their properties. Then we introduce the `higher topological complexity' and `weak higher topological…

math.AT2020★ 1 cited

Maps of degree one, relative LS category and higher topological complexities

Yuli B. Rudyak, Soumen Sarkar

In this paper, we introduce relative LS category of a map and study some of its properties. Then we introduce `higher topological complexity' of a map, a homotopy invariant. We giv…

math.AT2017

Cohomological Dimension, Connectivity, and Lusternik--Schnirelmann category

Yuli Rudyak

Dranishnikov~\cite{D2} proved that \[{\rm cat} X\leq {\rm cd}(π_1(X))+\Bigl\lceil\frac{{\rm hd} (X)-1}{2}\Bigr\rceil.\] where $cd (π)$ denotes the cohomological dimension of a…