Zobrazeno 1 - 10
of 93
pro vyhledávání: '"Rudyak, Yuli B."'
Autor:
Kundu, Deep, Rudyak, Yuli B.
Let $Crit M$ denote the minimal number of critical points (not necessarily non-degenerate) on a closed smooth manifold $M$. We are interested in the evaluation of $Crit$. It is worth noting that we do not know yet whether $Crit M$ is a homotopy invar
Externí odkaz:
http://arxiv.org/abs/2306.07942
Autor:
Rudyak, Yuli B.
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 $X$. We can interpret $p(A)$ as the probability of openness of $A$.
Externí odkaz:
http://arxiv.org/abs/2212.00063
Autor:
Rudyak, Yuli B., Sarkar, Soumen
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 complexity' of a map. Each of them are homotopy invariants. We discus
Externí odkaz:
http://arxiv.org/abs/2112.00983
Autor:
Kundu, Deep, Rudyak, Yuli B.
Publikováno v:
In Topology and its Applications 15 February 2024 343
Autor:
Rudyak, Yuli B., Sarkar, Soumen
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 give a cohomological lower bound and compare it with previously known `to
Externí odkaz:
http://arxiv.org/abs/2011.13531
Autor:
Rudyak, Yuli B., Sarkar, Soumen
Publikováno v:
In Topology and its Applications 1 December 2022 322
Publikováno v:
Algebr. Geom. Topol. 14 (2014) 2103-2124
We develop the properties of the $n$-th sequential topological complexity $TC_n$, a homotopy invariant introduced by the third author as an extension of Farber's topological model for studying the complexity of motion planning algorithms in robotics.
Externí odkaz:
http://arxiv.org/abs/1009.1851
Autor:
Rudyak, Yuli B.
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 $\TC_2(X)=\TC(X)$ and $\TC_n(X)\le \TC_{n+1}(X)$. For these higher complexi
Externí odkaz:
http://arxiv.org/abs/0909.1616
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 the inequality in the opposite direction. In particular, combining our
Externí odkaz:
http://arxiv.org/abs/0812.4637
Given a closed manifold M, we prove the upper bound of (n+d)/2 for the length of a product of systoles that can form a curvature-free lower bound for the total volume of M, in the spirit of M. Gromov's systolic inequalities. Here n is the dimension o
Externí odkaz:
http://arxiv.org/abs/0807.5040