Related papers: Simplicial moves on complexes and manifolds

A celebrated result concerning triangulations of a given closed 3-manifold is that any two triangulations with the same number of vertices are connected by a sequence of so-called 2-3 and 3-2 moves. A similar result is known for ideal…

We use intuitive results from algebraic topology and intersection theory to clarify the pullback action on cohomology by compositions of rational maps. We use these techniques to prove a simple sufficient criterion for functoriality of a…

For any orbifold M, we explicitly construct a simplicial complex S(M) from a given triangulation of the `coarse' underlying space together with the local isotropy groups of M. We prove that, for any local system on M, this complex S(M) has…

We prove that a connected simplicial complex is uniquely determined by its complex of discrete Morse functions. This settles a question raised by Chari and Joswig. In the 1-dimensional case, this implies that the complex of rooted forests…

Let $d\in {\mathbb N}$ and $p_i$ be an integral polynomial with $p_i(0)=0$, $1\le i\le d$. It is shown that if $S$ is piecewise syndetic in $\mathbb Z$, then $$\{(m,n)\in{\mathbb Z}^2: m+p_1(n),\ldots,m+p_d(n)\in S\}$$ is piecewise syndetic…

There are a large number of theorems detailing the homological properties of the Stanley--Reisner ring of a simplicial complex. Here we attempt to generalize some of these results to the case of a simplicial poset. By investigating the…

In this paper we relate the study of actions of discrete groups over connected manifolds to that of their orbit spaces seen as differentiable stacks. We show that the orbit stack of a discrete dynamical system on a simply connected manifold…

We describe an elementary combinatorial move on the set of quadratic differentials with a horizontal one cylinder decom-position. Computer experiment suggests that the corresponding equivalent classes are in one-to-one correspondence with…

For any positive integer $n$, Lov\'{a}sz-Schrijver, Taniyama and Skopenkov provided examples of simplicial $n$-complexes that inevitably contain a nonsplittable two-component link of $n$-spheres, no matter how they are embedded into the…

This paper is a continuation of our previous work in which we defined the notion of a polytope complex and its $K$-theory. In this paper we produce formulas for the delooping of a simplicial polytope complex and the cofiber of a morphism of…

This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/topological origins. It is intended to be accessible to…

Scalar-tensor theories are one of the most natural and well-constrained alternative theories of gravity, while still allowing for significant deviations from general relativity. We present the equations of motion of nonspinning compact…

It is proved that a triangulation of a polyhedron can always be transformed into any other triangulation of the polyhedron by using only elementary moves. One consequence is that an additive function (valuation) defined only on simplices…

We prove that every simplicial complex is the dual complex of some simple normal crossing divisor in a smooth variety. As an application, we simplify and extend the results of Kapovich--Koll\'ar (math.AG:1109.4047) on the existence of…

We use double categories to obtain a single theorem characterizing certain exponentiable morphisms of small categories, topological spaces, locales, and posets.

We use the topology of simplicial complexes to model political structures following [1]. Simplicial complexes are a natural tool to encode interactions in the structures since a simplex can be used to represent a subset of compatible…

We investigate some combinatorial properties of convex polytopes simple in edges. For polytopes whose nonsimple vertices are located sufficiently far one from another, we prove an analog of the Hard Lefschetz theorem. It implies Stanley's…

We consider a class of right-angled Coxeter orbifolds, named as simple orbifolds, which are a generalization of simple polytopes. Similarly to manifolds over simple polytopes, the topology and geometry of manifolds over simple orbifolds are…

The dual complex of a singularity is defined, up-to homotopy, using resolutions of singularities. In many cases, for instance for isolated singularities, we identify and study a "minimal" representative of the homotopy class that is well…

Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…