Related papers: Models for Configuration Space in a Simplicial Com…
We construct a real combinatorial model for the configuration spaces of points of compact smooth oriented manifolds without boundary. We use these models to show that the real homotopy type of configuration spaces of a simply connected such…
Simplicial complexes are generalized network structures able to encode interactions occurring between more than two nodes. Simplicial complexes describe a large variety of complex interacting systems ranging from brain networks, to social…
From a group action on a space, define a variant of the configuration space by insisting that no two points inhabit the same orbit. When the action is almost free, this "orbit configuration space" is the complement of an arrangement of…
We investigate the collapsibility of systolic finite simplicial complexes of arbitrary dimension. The main tool we use in the proof is discrete Morse theory. We shall consider a convex subcomplex of the complex and project any simplex of…
In this work we present a new methodology to study the structure of the configuration spaces of hard combinatorial problems. It consists in building the network that has as nodes the locally optimal configurations and as edges the weighted…
Simplicial complexes are a popular tool used to model higher-order interactions between elements of complex social and biological systems. In this paper, we study some combinatorial aspects of a class of simplicial complexes created by a…
We construct a model structure on the category of ordered simplicial complexes, Quillen equivalent to the standard model structure on simplicial sets. This shows that simplicial complexes, which are fully combinatorial in nature, provide a…
Simplicial complexes are higher-order combinatorial structures which have been used to represent real-world complex systems. In this paper, we concentrate on the local patterns in simplicial complexes called simplets, a generalization of…
In this, largely expository, note, we show how the simplicial structure of the moduli spaces of stable rational curves with marked points allows to produce explicit equations for these spaces. The key argument is an elementary combinatorial…
We study a number of local and global classification problems in generalized complex geometry. In the first topic, we characterize the local structure of generalized complex manifolds by proving that a generalized complex structure near a…
Configuration spaces of many real mechanical systems appear to be manifolds with singularity. A singularity often indicates that geometry of motion may change at the singular point of configuration space. We face conceptual problem…
Given a simplicial complex $X$, we construct a simplicial complex $\Omega X$ that may be regarded as a combinatorial version of the based loop space of a topological space. Our construction explicitly describes the simplices of $\Omega X$…
We study configuration spaces of framed points on oriented closed smooth manifolds. Such configuration spaces admit natural actions of the framed little discs operads, that play an important role in the study of embedding spaces of…
W. Fulton and R. MacPherson described a Sullivan dg-algebra model for the space of n-configurations of labeled points in a smooth compact complex algebraic variety X. I. Kriz then gave a simpler model that depends only on the cohomology…
We study the problem of computing the homology of the configuration spaces of a finite cell complex $X$. We proceed by viewing $X$, together with its subdivisions, as a subdivisional space--a kind of diagram object in a category of cell…
We compute small rational models for configuration spaces of points on oriented surfaces, as right modules over the framed little disks operad. We do this by splitting these surfaces in unions of several handles. We first describe rational…
It is well known that not every combinatorial configuration admits a geometric realization with points and lines. Moreover, some of them do not even admit realizations with pseudoline arrangements, i.e., they are not topological. In this…
This paper begins by extending the notion of a combinatorial configuration of points and lines to a combinatorial configuration of points and planes that we refer to as configurations of order $2$. We then proceed to investigate a further…
We find an explicit combinatorial gradient vector field on the well known complex S (Salvetti complex) which models the complement to an arrangement of complexified hyperplanes. The argument uses a total ordering on the facets of the…
The notion of regular cell complexes plays a central role in topological combinatorics because of its close relationship with posets. A generalization, called totally normal cellular stratified spaces, was introduced by the third author by…