Simplicial Sets from Categories.
Simplicial T-complexes and crossed complexes: a non-abelian version of a theorem of Dold and Kan [Book]
Simplicial types and polynomial algebras
This paper shows that the simplicial type of a finite simplicial complex is determined by its algebra of polynomial functions on the baricentric coordinates with coefficients in any integral domain. The link between and is done through certain admissible matrix associated to in a natural way. This result was obtained for the real numbers by I. V. Savel’ev [5], using methods of real algebraic geometry. D. Kan and E. Miller had shown in [2] that determines the homotopy type of the polyhedron...
Simply connected coset complexes for rank 1 groups of Lie type.
Some geometric perspectives in concurrency theory.
Sur les limites homotopiques de diagrammes homotopiquement cohérents
Systolic invariants of groups and -complexes via Grushko decomposition
We prove a finiteness result for the systolic area of groups. Namely, we show that there are only finitely many possible unfree factors of fundamental groups of -complexes whose systolic area is uniformly bounded. We also show that the number of freely indecomposable such groups grows at least exponentially with the bound on the systolic area. Furthermore, we prove a uniform systolic inequality for all -complexes with unfree fundamental group that improves the previously known bounds in this dimension....
The branching nerve of HDA and the Kan condition.
The cohomology ring of free loop spaces.
The fundamental group of balanced simplicial complexes and posets.
The moduli space of n tropically collinear points in Rd.
The tropical semiring (R, min, +) has enjoyed a recent renaissance, owing to its connections to mathematical biology as well as optimization and algebraic geometry. In this paper, we investigate the space of labeled n-point configurations lying on a tropical line in d-space, which is interpretable as the space of n-species phylogenetic trees. This is equivalent to the space of n x d matrices of tropical rank two, a simplicial complex. We prove that this simplicial complex is shellable for dimension...
The S1-CW decomposition of the geometric realization of a cyclic set
We show that the geometric realization of a cyclic set has a natural, -equivariant, cellular decomposition. As an application, we give another proof of a well-known isomorphism between cyclic homology of a cyclic space and -equivariant Borel homology of its geometric realization.
The tropical Grassmannian.
Un ejemplo de teoría de homotopía en los grupos abelianos.
Un groupoïde simplicial comme modèle de l'espace des chemins
Un théorême sur les sommes amalgamées de groupes simpliciaux.
Unicite de la suite spectrale d'un fibre.
Когомологии малых категорий с коэффициентами в абелевой категории с точными произведениями.