Zobrazeno 1 - 10
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pro vyhledávání: '"Dranishnikov, Alexander"'
Autor:
Dranishnikov, Alexander
We study numerical invariants $d\TC(\Gamma)$ and $d\cat(\Gamma)$ of groups recently introduced in \cite{DJ} and independently in \cite{KW}. We compute $d\TC$ for finite cyclic groups $\mathbb Z_p$ with prime $p$ as well as for nonorientable surfaces
Externí odkaz:
http://arxiv.org/abs/2404.03041
We define a new version of Topological Complexity (TC) of a space, denoted as $\text{dTC}$, which, we think, fits better for motion planning for some autonomous systems. Like Topological complexity, \text{dTC} is also a homotopy invariant. Also, $\te
Externí odkaz:
http://arxiv.org/abs/2401.04272
Autor:
Dranishnikov, Alexander
We introduce the notion of Lipschitz cohomology classes of a group with local coefficients and reduce the Novikov higher signature conjecture for a group $\Gamma$ to the question whether the Berstein-Schwarz class $\beta_\Gamma\in H^1(\Gamma,I(\Gamma
Externí odkaz:
http://arxiv.org/abs/2311.12637
We prove that the universal covering $\Wi M$ of an $n$-dimensional closed spin PSC manifold $M$ whose fundamental group $\pi_1(M)$ is a right-angled Artin group has macroscopic dimension $\dim_{mc}\Wi M\le n-2$. This confirms Gromov's conjecture in t
Externí odkaz:
http://arxiv.org/abs/2311.00573
The (co)homological dimension of homomorphism $\phi:G\to H$ is the maximal number $k$ such that the induced homomorphism is nonzero for some $H$-module. The following theorems are proven: THEOREM 1. For every homomorphism $\phi:G\to H$ of a geometric
Externí odkaz:
http://arxiv.org/abs/2302.09686
The Higson compactification of any simply connected proper geodesic metric space admits an embedding into a product of adelic solenoids that induces an isomorphism of 1-dimensional cohomology.
Externí odkaz:
http://arxiv.org/abs/2205.03698
We prove the equality $\cat(\phi)=\cd(\phi)$ for homomorphisms $\phi:\Gamma\to \Lambda$ of a torsion free finitely generated nilpotent groups $\Gamma$ to an arbitrary group $\Lambda$. We construct an epimorphism $\psi:G\to H$ between geometrically fi
Externí odkaz:
http://arxiv.org/abs/2203.03734
Autor:
Dranishnikov, Alexander
We prove that a closed $n$-manifold $M$ with positive scalar curvature and abelian fundamental group admits a finite covering $M'$ which is strongly inessential. The latter means that a classifying map $u:M'\to K(\pi_1(M'),1)$ can be deformed to the
Externí odkaz:
http://arxiv.org/abs/2105.07528
Autor:
Dranishnikov, Alexander
In ~\cite{Iw2} Iwase has constructed two 16-dimensional manifolds $M_2$ and $M_3$ with LS-category 3 which are counter-examples to Ganea's conjecture: ${\rm cat_{LS}} (M\times S^n)={\rm cat_{LS}} M+1$. We show that the manifold $M_3$ is a counter-exa
Externí odkaz:
http://arxiv.org/abs/2011.04819