Expand all Collapse all | Results 1 - 8 of 8 |
1. CMB 2013 (vol 57 pp. 245)
Assouad-Nagata Dimension of Wreath Products of Groups Consider the wreath product $H\wr G$, where $H\ne 1$ is finite and $G$ is finitely generated.
We show that the Assouad-Nagata dimension $\dim_{AN}(H\wr G)$ of $H\wr G$
depends on the growth of $G$ as follows:
\par If the growth of $G$ is not bounded by a linear function, then $\dim_{AN}(H\wr G)=\infty$,
otherwise $\dim_{AN}(H\wr G)=\dim_{AN}(G)\leq 1$.
Keywords:Assouad-Nagata dimension, asymptotic dimension, wreath product, growth of groups Categories:54F45, 55M10, 54C65 |
2. CMB 2013 (vol 57 pp. 335)
Alexandroff Manifolds and Homogeneous Continua ny homogeneous,
metric $ANR$-continuum is a $V^n_G$-continuum provided $\dim_GX=n\geq
1$ and $\check{H}^n(X;G)\neq 0$, where $G$ is a principal ideal
domain.
This implies that any homogeneous $n$-dimensional metric $ANR$-continuum is a $V^n$-continuum in the sense of Alexandroff.
We also prove that any finite-dimensional homogeneous metric continuum
$X$, satisfying $\check{H}^n(X;G)\neq 0$ for some group $G$ and $n\geq
1$, cannot be separated by
a compactum $K$ with $\check{H}^{n-1}(K;G)=0$ and $\dim_G K\leq
n-1$. This provides a partial answer to a question of
Kallipoliti-Papasoglu
whether any two-dimensional homogeneous Peano continuum cannot be separated by arcs.
Keywords:Cantor manifold, cohomological dimension, cohomology groups, homogeneous compactum, separator, $V^n$-continuum Categories:54F45, 54F15 |
3. CMB 2011 (vol 56 pp. 92)
On Perturbations of Continuous Maps We give sufficient conditions for the following problem: given a
topological space $X$, a metric space $Y$, a subspace $Z$ of $Y$, and
a continuous map $f$ from $X$ to $Y$, is it possible, by applying to
$f$ an arbitrarily small perturbation, to ensure that $f(X)$ does not
meet $Z$? We also give a relative variant: if $f(X')$ does not meet
$Z$ for a certain subset $X'\subset X$, then we may keep $f$ unchanged
on $X'$. We also develop a variant for continuous sections of
fibrations and discuss some applications to matrix perturbation
theory.
Keywords:perturbation theory, general topology, applications to operator algebras / matrix perturbation theory Category:54F45 |
4. CMB 2010 (vol 53 pp. 629)
Asymptotic Dimension of Proper CAT(0) Spaces that are Homeomorphic to the Plane In this paper, we investigate
a proper CAT(0) space $(X,d)$
that is homeomorphic to $\mathbb R^2$ and
we show that the asymptotic dimension $\operatorname{asdim} (X,d)$ is
equal to $2$.
Keywords:asymptotic dimension, CAT(0) space, plane Categories:20F69, 54F45, 20F65 |
5. CMB 2010 (vol 53 pp. 438)
Near-Homeomorphisms of Nöbeling Manifolds We characterize maps between $n$-dimensional NÃ¶beling manifolds that can be approximated by homeomorphisms.
Keywords:n-dimensional Nöbeling manifold, Z-set unknotting, near-homeomorphism Categories:55M10, 54F45 |
6. CMB 2005 (vol 48 pp. 614)
On Finite-to-One Maps Let $f\colon X\to Y$ be a $\sigma$-perfect $k$-dimensional surjective
map of metrizable spaces such that $\dim Y\leq m$. It is shown that
for every positive integer $p$ with $ p\leq m+k+1$ there exists a
dense $G_{\delta}$-subset ${\mathcal H}(k,m,p)$ of $C(X,\uin^{k+p})$
with the source limitation topology such that each fiber of
$f\triangle g$, $g\in{\mathcal H}(k,m,p)$, contains at most
$\max\{k+m-p+2,1\}$ points. This result
provides a proof the following conjectures of
S. Bogatyi, V. Fedorchuk and J. van Mill.
Let $f\colon X\to Y$ be a $k$-dimensional map between compact
metric spaces with $\dim Y\leq m$. Then:
\begin{inparaenum}[\rm(1)]
\item there exists a map
$h\colon X\to\uin^{m+2k}$ such that $f\triangle h\colon X\to
Y\times\uin^{m+2k}$ is 2-to-one provided $k\geq 1$;
\item there exists a
map $h\colon X\to\uin^{m+k+1}$ such that $f\triangle h\colon X\to
Y\times\uin^{m+k+1}$ is $(k+1)$-to-one.
\end{inparaenum}
Keywords:finite-to-one maps, dimension, set-valued maps Categories:54F45, 55M10, 54C65 |
7. CMB 2001 (vol 44 pp. 266)
Extension of Maps to Nilpotent Spaces We show that every compactum has cohomological dimension $1$ with respect
to a finitely generated nilpotent group $G$ whenever it has cohomological
dimension $1$ with respect to the abelianization of $G$. This is applied
to the extension theory to obtain a cohomological dimension theory condition
for a finite-dimensional compactum $X$ for extendability of every map from
a closed subset of $X$ into a nilpotent $\CW$-complex $M$ with finitely
generated homotopy groups over all of $X$.
Keywords:cohomological dimension, extension of maps, nilpotent group, nilpotent space Categories:55M10, 55S36, 54C20, 54F45 |
8. CMB 2001 (vol 44 pp. 80)
Constructing Compacta of Different Extensional Dimensions Applying the Sullivan conjecture we construct compacta of certain
cohomological and extensional dimensions.
Keywords:cohomological dimension, Eilenberg-MacLane complexes, Sullivan conjecture Categories:55M10, 54F45, 55U20 |