相关论文: A triangulation of $\CC P^3$ as symmetric cube of …

We present two constructions in this paper: (a) A 10-vertex triangulation $\CC P^{2}_{10}$ of the complex projective plane $\CC P^{2}$ as a subcomplex of the join of the standard sphere ($S^{2}_4$) and the standard real projective plane…

According to a well-known result in geometric topology, we have \linebreak $\left (\mathbb{S}^2 \right)^{n}\!\!/\operatorname{Sym}(n) = \mathbb{CP}^{n}$, where $\operatorname{Sym}(n)$ acts on $\left (\mathbb{S}^2 \right)^{n}$ by coordinate…

In this paper our main result states that there exist exactly three combinatorially distinct centrally-symmetric 12-vertex-triangulations of the product of two 2-spheres with a cyclic symmetry. We also compute the automorphism groups of the…

We present a $6$-dimensional centrally symmetric simplicial polytope for which the antipodal quotient of its boundary forms a $24$-vertex triangulation of the $5$-dimensional real projective space. This $6$-polytope is highly symmetric with…

We consider causal 3-dimensional triangulations with the topology of $S^2\times [0,1]$ or $D^2\times [0,1]$ where $S^2$ and $D^2$ are the two-dimensional sphere and disc, respectively. These triangulations consist of slices and we show that…

In combinatorial topology we aim to triangulate manifolds such that their topological properties are reflected in the combinatorial structure of their description. Here, we give a combinatorial criterion on when exactly triangulations of…

We construct a 3-dimensional cell complex that is the 3-skeleton for an Eilenberg--MacLane classifying space for the symmetric group $\mathfrak{S}_n$. Our complex starts with the presentation for $\mathfrak{S}_n$ with $n-1$ adjacent…

A free action of the direct product of two copies of the symmetric group on 3 elements on the cartesian product of two copies of the 3-sphere is constructed. This nonlinear action is constructed using surgery. The action provides a…

The 4-dimensional abstract Kummer variety K^4 with 16 nodes leads to the K3 surface by resolving the 16 singularities. Here we present a simplicial realization of this minimal resolution. Starting with a minimal 16-vertex triangulation of…

Simplicial approximation provides a framework for constructing simplicial complexes that are homotopy equivalent to a given manifold, provided a CW structure is explicitly known. However, its conventional implementation quickly becomes…

In this paper we construct and study a new 15-vertex triangulation $X$ of the complex projective plane $\CP^2$. The automorphism group of $X$ is isomorphic to $S_4\times S_3$. We prove that the triangulation $X$ is the minimal by the number…

Causal dynamical triangulations (CDT) constitute a background independent, nonperturbative approach to quantum gravity, in which the gravitational path integral is approximated by the weighted sum over causally well-behaving simplicial…

Let $p \geq 3$ be a prime integer and, for $l \geq 1$, let $G \cong {\mathbb Z}_{p}^{l}$ be a group of conformal automorphisms of some closed Riemann surface $S$ of genus $g \geq 2$. By the Riemann-Hurwitz formula, either $p \leq g+1$ or…

Let $\langle I_{1}, I_{2}, I_{3}\rangle$ be the complex hyperbolic $(4,4,\infty)$ triangle group. In this paper we give a proof of a conjecture of Schwartz for $\langle I_{1}, I_{2}, I_{3}\rangle$. That is $\langle I_{1}, I_{2},…

A product of a K3 surface $S$ and a flat 3-dimensional torus $T^3$ is a manifold with holonomy $SU(2)$. Since $SU(2)$ is a subgroup of $G_2$, $S\times T^3$ carries a torsion-free $G_2$-structure. We assume that $S$ admits an action of…

We construct an explicit diffeomorphism between the Sasaki-Einstein spaces Y^{p,q} and the product space S^3 \times S^2 in the cases q \le 2. When q=1 we express the K\"ahler quotient coordinates as an SU(2) bundle over S^2 which we…

This paper's theme is the relation between several classical and well-known objects: triangle Fuchsian groups, quasi-homogeneous singularities of plane curves, torus knot complements in the 3-sphere. Torus knots are the only nontrivial…

In the present paper we show that it is possible to obtain the well known Pauli group $P=\langle X,Y,Z \ | \ X^2=Y^2=Z^2=1, (YZ)^4=(ZX)^4=(XY)^4=1 \rangle $ of order $16$ as an appropriate quotient group of two distinct spaces of orbits of…

In this paper, we study $Z_2$ actions on a cell complex X having the cohomology ring isomorphic to that of the wedge sum $P^2 (n) V S^{3n}$ or $S^n V S^{2n} V S^{3n}$. We determine the possible fixed point sets depending on whether or not X…

We present small triangulations of all connected sums of $\mathbb{CP}^2$ and $S^2 \times S^2$ with the standard piecewise linear structure. Our triangulations have $2\beta_2+2$ pentachora, where $\beta_2$ is the second Betti number of the…