45 citations · 175 across the 43 of their papers we have counts for
18 papers · 1 filter
On spaces of minimal higher topological complexity
Yuli Rudyak
Let TC(X) denote the n-th topological complexity of a topological space X. It is known that TC(X) does not exceed n-1 for non-contractible X, and so it makes sense to descr…
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…
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…
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 denotes the cohomological dimension of a…
Symplectic Asphericity, Category Weight, and Closed Characteristics of K-Contact Manifolds
Yuli Rudyak, Aleksy Tralle
Let be a closed K-contact -manifold equipped with a quasi-regular K-contact structure. Rukimbira proved that the Reeb vector field of this structure has at least $n…
Maps of Degree 1 and Lusternik--Schnirelmann Category
Yuli Rudyak
Given a map of degree 1 of closed manifolds. Is it true that the Lusternik--Schnirelmann category of the range of the map is not more that the category of the domain?…
On topological complexity of Eilenberg-MacLane spaces
Yuli Rudyak
We note that, for any natural and every natural between and , there exists a group with $\cat K(π,1)=k$ and $\TC(K(π,1))=l$. Because of this, we can set up a pr…
Higher topological complexity and its symmetrization
Ibai Basabe, Jesus Gonzalez, Yuli B. Rudyak +1
We develop the properties of the -th sequential topological complexity , a homotopy invariant introduced by the third author as an extension of Farber's topological model…
On higher analogs of topological complexity
Yuli B. Rudyak
Farber introduced a notion of topological complexity $\TC(X)$ that is related to robotics. Here we introduce a series of numerical invariants $\TC_n(X), n=1,2, ...$ such that $\TC_…
Stable Systolic Category of Manifolds and the Cup-length
Alexander N. Dranishnikov, Yuli B. Rudyak
It follows from a theorem of Gromov that the stable systolic category of a closed manifold is bounded from below by the rational cup-length of the manifold. In the paper we study t…
Small values of the Lusternik-Schnirelmann category for manifolds
Alexander N. Dranishnikov, Mikhail G. Katz, Yuli B. Rudyak
We prove that manifolds of Lusternik-Schnirelmann category 2 necessarily have free fundamental group. We thus settle a 1992 conjecture of Gomez-Larranaga and Gonzalez-Acuna, by gen…
On the Berstein-Svarc Theorem in dimension 2
Alexander N. Dranishnikov, Yuli B. Rudyak
We prove that for any group of the cohomological dimension the th power of the Berstein class of the group is nontrivial. This allows to prove the following Berstein-Svarc t…
Small values of Lusternik-Schnirelmann and systolic categories for manifolds
Alexander N. Dranishnikov, Mikhail G. Katz, Yuli B. Rudyak
We prove that manifolds of Lusternik-Schnirelmann category 2 necessarily have free fundamental group. We thus settle a 1992 conjecture of Gomez-Larranaga and Gonzalez-Acuna, by gen…
Fundamental groups of compact Hausdorff spaces
James E. Keesling, Yuli B. Rudyak
We discuss which groups can be realized as the fundamental groups of compact Hausdorff spaces. In particular, we prove that the claim ``every group can be realized as the fundament…
Examples of non-formal closed -connected manifolds of dimensions and more
Alex N. Dranishnikov, Yuli B. Rudyak
We construct closed -connected manifolds of dimensions that possess non-trivial rational Massey triple products. We also construct examples of manifolds such…
Detecting Elements and Lusternik--Schnirelmann Category of 3-Manifolds
John Oprea, Yuli Rudyak
In this paper, we give a new simplified calculation of the Lusternik-Schnirelmann category of closed 3-manifolds. We also describe when 3-manifolds have detecting elements and prov…
On sequences cat (f\sp k)
Yuli B. Rudyak
We prove that, for every decreasing sequence {a \sb k} of natural numbers, there exists a map f: X --> X with cat (f\sp k)=a\sb k.
Piecewise linear structures on topological manifolds
Yuli B. Rudyak
This is a survey paper where we expose the Kirby--Siebenmann results on classification of PL structures on topological manifolds and, in particular, the homotopy equivalence TOP/PL…