32 research outputs found
On noncontractible compacta with trivial homology and homotopy groups
We construct an example of a Peano continuum such that: (i) is a
one-point compactification of a polyhedron; (ii) is weakly homotopy
equivalent to a point (i.e. is trivial for all ); (iii)
is noncontractible; and (iv) is homologically and cohomologically
locally connected (i.e. is a and space). We also prove that all
classical homology groups (singular, \v{C}ech, and Borel-Moore), all classical
cohomology groups (singular and \v{C}ech), and all finite-dimensional Hawaiian
groups of are trivial
On nerves of fine coverings of acyclic spaces
The main results of this paper are: (1) If a space can be embedded as a
cellular subspace of then admits arbitrary fine open
coverings whose nerves are homeomorphic to the -dimensional cube
; (2) Every -dimensional cell-like compactum can be embedded
into -dimensional Euclidean space as a cellular subset; and (3) There
exists a locally compact planar set which is acyclic with respect to \v{C}ech
homology and whose fine coverings are all nonacyclic
On the second homotopy group of
In our earlier paper (K. Eda, U. Karimov, and D. Repov\v{s}, \emph{A
construction of simply connected noncontractible cell-like two-dimensional
Peano continua}, Fund. Math. \textbf{195} (2007), 193--203) we introduced a
cone-like space . In the present note we establish some new algebraic
properties of
On Snake cones, Alternating cones and related constructions
We show that the Snake on a square is homotopy equivalent to the
space which was investigated in the previous work by Eda, Karimov and
Repov\vs. We also introduce related constructions and and
investigate homotopical differences between these four constructions. Finally,
we explicitly describe the second homology group of the Hawaiian tori wedge
A nonaspherical cell-like 2-dimensional simply connected continuum and related constructions
We prove the existence of a 2-dimensional nonaspherical simply connected
cell-like Peano continuum (the space itself was constructed in one of our
earlier papers). We also indicate some relations between this space and the
well-known Griffiths' space from the 1950's
On the fundamental group of R^3 modulo the Chase-Chaberlin continuum
It has been known for a long time that the fundamental group of the quotient of R^3 by the Case-Chamberlin continuum is nontrivial. In the present paper we prove that this group is in fact, uncountable