Zobrazeno 1 - 10
of 238
pro vyhledávání: '"Cencelj, M."'
In this survey we present applications of the ideas of complement and neighborhood in the theory embeddings of manifolds into Euclidean space (in codimension at least three). We describe how the combination of these ideas gives a reduction of embedda
Externí odkaz:
http://arxiv.org/abs/2104.01820
Publikováno v:
Topology Appl. 239 (2018), 226-233
It is well-known that a paracompact space $X$ is of covering dimension at most $n$ if and only if any map $f\colon X\to K$ from $X$ to a simplicial complex $K$ can be pushed into its $n$-skeleton $K^{(n)}$. We use the same idea to characterize asympt
Externí odkaz:
http://arxiv.org/abs/1508.01460
Recent research in coarse geometry revealed similarities between certain concepts of analysis, large scale geometry, and topology. Property A of G.Yu is the coarse analog of amenability for groups and its generalization (exact spaces) was later stren
Externí odkaz:
http://arxiv.org/abs/1208.2864
Publikováno v:
Rev. Mat. Complut. 26 (2013), no. 2 561-571
It is well-known that a paracompact space X is of covering dimension n if and only if any map f from X to a simplicial complex K can be pushed into its n-skeleton. We use the same idea to define dimension in the coarse category. It turns out the anal
Externí odkaz:
http://arxiv.org/abs/0909.4095
Publikováno v:
Topology and its Applications 159(2012), 646-658
Using ideas from shape theory we embed the coarse category of metric spaces into the category of direct sequences of simplicial complexes with bonding maps being simplicial. Two direct sequences of simplicial complexes are equivalent if one of them c
Externí odkaz:
http://arxiv.org/abs/0906.1372
Publikováno v:
Glas. Mat. Ser. III 47 (2012), no. 2, 441-444
The purpose of this note is to characterize the asymptotic dimension $asdim(X)$ of metric spaces $X$ in terms similar to Property A of Yu: If $(X,d)$ is a metric space and $n\ge 0$, then the following conditions are equivalent: [a.] $asdim(X,d)\leq n
Externí odkaz:
http://arxiv.org/abs/0812.2619
Publikováno v:
Sbornik: Mathematics 203:11 (2012), 1654-1681
This paper is on the classical Knotting Problem: for a given manifold N and a number m describe the set of isotopy classes of embeddings $N\to S^m$. We study the specific case of knotted tori, i. e. the embeddings $S^p \times S^q \to S^m$. The classi
Externí odkaz:
http://arxiv.org/abs/0811.2745
Publikováno v:
Proceedings of the American Math.Soc. 138 (2010), 1501-1510
We extend the definition of Bockstein basis $\sigma(G)$ to nilpotent groups $G$. A metrizable space $X$ is called a {\it Bockstein space} if $\dim_G(X) = \sup\{\dim_H(X) | H\in \sigma(G)\}$ for all Abelian groups $G$. Bockstein First Theorem says tha
Externí odkaz:
http://arxiv.org/abs/0809.3957
Publikováno v:
Russian Math. Surv. 62:5 (2007), 985-987
This paper is devoted to the classification of embeddings of higher dimensional manifolds. We study the case of embeddings $S^p\times S^q\to S^m$, which we call knotted tori. The set of knotted tori in the the space of sufficiently high dimension, na
Externí odkaz:
http://arxiv.org/abs/0803.4285
Publikováno v:
Topology Appl. 156:13 (2009), 2175-2188.
We prove that Dranishnikov's $k$-dimensional resolution $d_k\colon \mu^k\to Q$ is a UV$^{n-1}$-divider of Chigogidze's $k$-dimensional resolution $c_k$. This fact implies that $d_k^{-1}$ preserves $Z$-sets. A further development of the concept of UV$
Externí odkaz:
http://arxiv.org/abs/0803.4126