相关论文: Small Covers over Prisms
In the present paper we find a bijection between the set of small covers over an $n$-cube and the set of acyclic digraphs with $n$ labeled nodes. Using this, we give a formula of the number of small covers over an $n$-cube (generally, a…
In this paper, based upon the basic theory for glued manifolds in M.W. Hirsch (1976) \cite[Chapter 8, \S 2 Gluing Manifolds Together]{h}, we give a method of constructing homeomorphisms between two small covers over simple convex polytopes.…
Given a dimension function $\omega$, we define a notion of an $\omega$-vector weighted digraph and an $\omega$-equivalence between them. Then we establish a bijection between the weakly $(\mathbb{Z}/2)^n$-equivariant homeomorphism classes…
In this paper, we compute the LS-category and equivariant LS-category of a small cover and its real moment angle manifold. We calculate a tight lower bound for the topological complexity of many small covers over a product of simplices.…
We introduce some compact orbifolds on which there is a certain finite group action having a simple convex polytope as the orbit space. We compute the orbifold fundamental group and homology groups of these orbifolds. We calculate the…
This paper contains a classication of the regular minimal abstract polytopes that act as covers for the convex polyhedral prisms and antiprisms. It includes a detailed discussion of their topological structure, and completes the enumeration…
In this paper we study the (equivariant) topological types of a class of 3-dimensional closed manifolds (i.e., 3-dimensional small covers), each of which admits a locally standard $(\mathbb{Z}_2)^3$-action such that its orbit space is a…
There are just 10 closed flat 3-manifolds, following [1], we call them platycosms. The aim of this paper is to classify types of n-coverings over amphicosms, i.e. some kinds of platycosms, and enumerate the numbers of them. Key words:…
In this paper the number of isomorphism classes of the right transversals of the symmetric group $\Sigma_{n-1}$ in the symmetric group $\Sigma_n$ is calculated. This result together with the techniques employed along the paper may be used…
In this note we derive enumerative formulas for several types of labelled acyclic directed graphs by slight modifications of the familiar recursive formula for simple acyclic digraphs. These considerations are motivated by, and based upon,…
We construct small covers and quasitoric manifolds over $n$-dimensional simple polytopes which allow proper colorings of facets with $n$ colors. We calculate Stiefel-Whitney classes of these manifolds as obstructions to immersions and…
We distinguish diffeomorphism types of relative trisections using a ``capping'' operation, which yields a trisection diagram of a closed 4-manifold from a relative trisection diagram. Using this operation, we give various examples of…
In this paper we prove an identity in terms of generating functions which enables us to calculate the numbers of isomorphism classes of absolutely indecomposable semistable representations of quivers over finite fields.
We count orientable small covers over cubes. We also get estimates for $O_n/R_n$, where $O_n$ is the number of orientable small covers and $R_n$ is the number of all small covers over an $n$-cube up to the Davis-Januszkiewicz equivalence.
There are a least uncountably many diffeomorphism types for open manifolds. Hence the classification problem is extremely difficult. We proceed as follows: We define several uniform structures of proper metric spaces and consider their arc…
In the present paper we consider preserving orientation Morse-Smale diffeomorphisms on surfaces. Using the methods of factorization and linearizing neighborhoods we prove that such diffeomorphisms have a finite number of orientable…
We present a way of constructing and deforming diffeomorphisms of manifolds endowed with a Lie group action. This is applied to the study of exotic diffeomorphisms and involutions of spheres and to the equivariant homotopy of Lie groups.
In this paper we give a full diffeomorphism characterization of compact simply connected cohomogeneity one manifolds in dimension six.
A crystallization of a PL manifold is an edge-colored graph that corresponds to a contracted triangulation of the manifold, facilitating the study of its topological and combinatorial properties. A small cover over a simple convex…
We study symplectic structures on four-dimensional small covers. Our main result shows that every symplectic four-dimensional small cover is aspherical. We then classify symplectic small covers over products of two polygons, proving that…