Zobrazeno 1 - 10
of 35
pro vyhledávání: '"BŁASZCZYK, ZBIGNIEW"'
The notion of effective topological complexity, introduced by B{\l}aszczyk and Kaluba, deals with using group actions in the configuration space in order to reduce the complexity of the motion planning algorithm. In this article we focus on studying
Externí odkaz:
http://arxiv.org/abs/2402.18524
Publikováno v:
Journal of Pure and Applied Algebra, Volume 226, Issue 6, June 2022, 106959
The sectional category of a subgroup inclusion $H \hookrightarrow G$ can be defined as the sectional category of the corresponding map between Eilenberg--MacLane spaces. We extend a characterization of topological complexity of aspherical spaces give
Externí odkaz:
http://arxiv.org/abs/2012.11912
Publikováno v:
In Journal of Pure and Applied Algebra June 2022 226(6)
Publikováno v:
Bull. Belg. Math. Soc. Simon Stevin 24, Number 4 (2017), 621-630
Let $G$ be a compact Lie group. We prove that if $V$ and $W$ are orthogonal $G$-representations such that $V^G=W^G=\{0\}$, then a $G$-equivariant map $S(V) \to S(W)$ exists provided that $\dim V^H \leq \dim W^H$ for any closed subgroup $H\subseteq G$
Externí odkaz:
http://arxiv.org/abs/1704.01656
Autor:
Błaszczyk, Zbigniew, Carrasquel, José
Publikováno v:
Rev. Mat. Iberoam. 34 (2018), 1679-1684
We introduce a variant of Farber's topological complexity, defined for smooth compact orientable Riemannian manifolds, which takes into account only motion planners with the lowest possible "average length" of the output paths. We prove that it never
Externí odkaz:
http://arxiv.org/abs/1607.00703
Autor:
Błaszczyk, Zbigniew, Kaluba, Marek
We explore transformation groups of manifolds of the form $M\times S^n$, where $M$ is an asymmetric manifold, i.e. a manifold which does not admit any non-trivial action of a finite group. In particular, we prove that for $n=2$ there exists an infini
Externí odkaz:
http://arxiv.org/abs/1603.04888
Publikováno v:
Topology Appl. 249 (2018), 112-126
We describe a unified approach to estimating the dimension of $f^{-1}(A)$ for any $G$-equivariant map $f \colon X \to Y$ and any closed $G$-invariant subset $A\subseteq Y$ in terms of connectivity of $X$ and dimension of $Y$, where $G$ is either a cy
Externí odkaz:
http://arxiv.org/abs/1512.02399
Autor:
Błaszczyk, Zbigniew, Kaluba, Marek
Publikováno v:
Publ. Mat. 62, Issue 1 (2018), 55-74
We introduce a version of Farber's topological complexity suitable for investigating mechanical systems whose configuration spaces exhibit symmetries. Our invariant has vastly different properties to the previous approaches of Colman-Grant, Dranishni
Externí odkaz:
http://arxiv.org/abs/1510.08724
Autor:
Błaszczyk, Zbigniew, Kaluba, Marek
Publikováno v:
Proc. Amer. Math. Soc. 145 (2017), 4075-4086
We investigate equivariant and invariant topological complexity of spheres endowed with smooth non-free actions of cyclic groups of prime order. We prove that semilinear $\mathbb{Z}/p$-spheres have both invariants either $2$ or $3$ and calculate exac
Externí odkaz:
http://arxiv.org/abs/1501.07724
Autor:
Błaszczyk, Zbigniew1 blaszczyk@amu.edu.pl, Kaluba, Marek1 kalmar@amu.edu.pl
Publikováno v:
Kyoto Journal of Mathematics. 2022, Vol. 62 Issue 4, p707-717. 11p.