Displaying similar documents to “Simplicial types and polynomial algebras”

Contractible simplicial objects

Michael Barr, John F. Kennison, Robert M. Raphael (2019)

Commentationes Mathematicae Universitatis Carolinae

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We raise the question of when a simplicial object in a catetgory is deemed contractible. The literature offers three definitions. One is the existence of an “extra degeneracy”, indexed by - 1 , which does not quite live up to the name. This can be strengthened to a “strong extra degeneracy". Another possibility is that it be homotopic to a constant simplicial object. Despite claims in the literature to the contrary, we show that all three are distinct concepts with strong extra degeneracy...

On the f - and h -triangle of the barycentric subdivision of a simplicial complex

Sarfraz Ahmad (2013)

Czechoslovak Mathematical Journal

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For a simplicial complex Δ we study the behavior of its f - and h -triangle under the action of barycentric subdivision. In particular we describe the f - and h -triangle of its barycentric subdivision sd ( Δ ) . The same has been done for f - and h -vector of sd ( Δ ) by F. Brenti, V. Welker (2008). As a consequence we show that if the entries of the h -triangle of Δ are nonnegative, then the entries of the h -triangle of sd ( Δ ) are also nonnegative. We conclude with a few properties of the h -triangle of sd ( Δ ) . ...

On G -disconnected injective models

Marek Golasiński (2003)

Annales de l’institut Fourier

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Let G be a finite group. It was observed by L.S. Scull that the original definition of the equivariant minimality in the G -connected case is incorrect because of an error concerning algebraic properties. In the G -disconnected case the orbit category 𝒪 ( G ) was originally replaced by the category 𝒪 ( G , X ) with one object for each component of each fixed point simplicial subsets X H of a G -simplicial set X , for all subgroups H ⊆ G . We redefine the equivariant minimality and redevelop some results on the...

A Weierstrass-Stone theorem for Choquet simplexes

David Alan Edwards, G. F. Vincent-Smith (1968)

Annales de l'institut Fourier

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Soit X ≠ ∅ un convexe compact d’un espace localement convexe séparé, soit A ( X ) l’espace de fonctions réelles affines continues sur X , et soit L un sous-espace de A ( X ) linéaire qui contient les fonctions constantes. Parmi les faces fermées de X sur lesquelles les fonctions de L sont toutes constantes on appelle les faces maximales L -faces. Nos théorèmes principaux donnent quelques conditions sous lesquelles L contient exactement ces fonctions qui sont constantes sur chaque L -face. En particulier,...

A general theory of polyhedral sets and the corresponding T-complexes

David W. Jones

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PrefaceThis paper is essentially David Jones' 1984 University of Wales Ph. D. Thesis, "Poly-T-complexes". It is published concurrently with Asley, 1988.The main aim is to find a setting for the most general kinds of geometrically defined compositions. Thus it comes under the slogan: "Find an algebraic inverse to subdivision". In the background is the Generalised Van Kampen Theorem, whose proof uses in an essential way general compositions of cubes. An even older background is the idea...

Moment-angle complexes from simplicial posets

Zhi Lü, Taras Panov (2011)

Open Mathematics

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We extend the construction of moment-angle complexes to simplicial posets by associating a certain T m-space Z S to an arbitrary simplicial poset S on m vertices. Face rings ℤ[S] of simplicial posets generalise those of simplicial complexes, and give rise to new classes of Gorenstein and Cohen-Macaulay rings. Our primary motivation is to study the face rings ℤ[S] by topological methods. The space Z S has many important topological properties of the original moment-angle complex Z K associated...