相关论文: On the second homotopy group of $SC(Z)$

In our earlier papers we constructed examples of 2-dimensional nonaspherical simply-connected cell-like Peano continua, called {\sl Snake space}. In the sequel we introduced the functor $SC(-,-)$ defined on the category of all spaces with…

We show that the Snake on a square $SC(S^1)$ is homotopy equivalent to the space $AC(S^1)$ which was investigated in the previous work by Eda, Karimov and Repov\vs. We also introduce related constructions $CSC(-)$ and $CAC(-)$ and…

Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all…

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…

We show that under suitable hypotheses, the second homotopy group of the coned-off space associated to a $C(9)$ cubical presentation is trivial, and use this to provide classifying spaces for proper actions for the fundamental groups of…

We show the vanishing of the second homotopy group of the \'etale homotopy type of a smooth connected algebraic group over a separably closed field, completed away from the characteristic. This is an algebraic analogue of a classical…

In this paper, we describe the structural properties of the cone of $\mathcal{Z}$-transformations on the second order cone in terms of the semidefinite cone and copositive/completely positive cones induced by the second order cone and its…

Secondary homotopy groups supplement the structure of classical homotopy groups. They yield a track functor on the track category of pointed spaces compatible with fiber sequences, suspensions and loop spaces. They also yield algebraic…

A smooth affine hypersurface Z of complex dimension n is homotopy equivalent to an n-dimensional cell complex. Given a defining polynomial f for Z as well as a regular triangulation of its Newton polytope, we provide a purely combinatorial…

We introduce so-called cone topologies of paratopological groups, which are a wide way to construct counterexamples, especially of examples of compact-like paratopological groups with discontinuous inversion. We found a simple interplay…

We discuss $\pmb{SC}_*$, a simplicial homotopy model of $K(Z,2)$ constructed from circular permutations. In any dimension, the number of simplices in the model is finite. The complex $\pmb{SC}_*$ naturally manifests as a simplicial set…

In this work, we are interested in a non symmetric homogeneous space, namely $SO(2m)/Sp(m)$. We show that this space admits a structure of $Z_2^2$-symmetric space. We describe all the non degenerated metrics and classify the Riemannian and…

We study the homotopy properties of the posets of p-subgroups Sp(G) and Ap(G) of a finite group G, viewed as finite topological spaces. We answer a question raised by R.E. Stong in 1984 about the relationship between the contractibility of…

We present new, unified proofs for the cell-like, $\mathbb{Z}/p$-, and $\mathbb{Q}$-resolution theorems. Our arguments employ extensions that are much simpler then those used by our predecessors. The techniques allow us to solve problems…

A finite connected CW complex which is a co-H-space is shown to have the homotopy type of a wedge of a bunch of circles and a simply-connected finite complex after almost $p$-completion at a prime $p$.

We demonstrate that companionships and conjunctions in double $\infty$-categories -- and more generally, in double Segal spaces -- extend to functors out of the free-living companionship and conjunction respectively. Specifically, we prove…

Described the algebraic structure on the space of homotopy classes of cycles with marked topological flags of disks. This space is a non-commutative monoid, with an Abelian quotient corresponding to the group of singular homologies…

We characterize those planar Peano continua that are homotopy equivalent to 1-dimensional sets. While many planar Peano continua are not homotopically 1-dimensional, we prove that each has fundamental group that embeds in the fundamental…

We apply our previous work on the relation between groupoid homology and K-theory to Smale spaces. More precisely, we consider the unstable equivalence relation of a Smale space with totally disconnected stable sets, and prove that the…

A class of Cantor-type spaces and related geometric structures are discussed.