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三亚国际数学论坛：Curvatures of Graphs,Simplicial Complexes and Metric Spaces（Curvatures of Graphs,Simplicial Complexes and Metric Spaces ）
三亚国际数学论坛 Curvatures of Graphs Simplicial Complexes Metric Spaces
2017/1/10
Curvature is a notion originally developed in differential and Riemannian geometry. It was then discovered that curvature inequalities in Riemannian manifolds are equivalent to other geometric propert...
The KH-Theory of Complete Simplicial Toric Varieties and the Algebraic K-Theory of Weighted Projective Spaces
Toric Varieties Algebraic K-Theory Weighted Projective Spaces K-regularity
2012/7/11
We show that, for a complete simplicial toric variety $X$, we can determine its homotopy $\K$-theory (denoted $\KH$-theory) entirely in terms of the torus pieces of open sets forming an open cover of ...
Square complexes and simplicial nonpositive curvature
Square complexes simplicial nonpositive curvature Group Theory
2011/9/16
Abstract: We prove that each nonpositively curved square VH-complex can be turned functorially into a locally 6-large simplicial complex of the same homotopy type. It follows that any group acting geo...
Abstract: The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The 3-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetime...
d-Representability of simplicial complexes of fixed dimension
Combinatorics d-Representability fixed dimension
2011/8/26
Abstract: Let K be a simplicial complex with vertex set V = {v_1,..., v_n}. The complex K is d-representable if there is a collection {C_1,...,C_n} of convex sets in R^d such that a subcollection {C_{...
Simplicial Homeology and Homeotopy
simplicial complex (co)homology (co)homeology homotopy homeotopy homeomorphism
2011/8/23
Abstract: In this paper, we define homeology group, reduced homeology group, cohomeology group and reduced cohomeology group on finite simpicial complexes and prove that these groups are homeomorphism...
A characterization of simplicial localization functors
characterization simplicial localization functors
2011/1/19
We characterize simplicial localization functors among relative functors from relative categories to simplicial categories as any choice of ho-motopy inverse to the delocalization functor of Dwyer and...
Simplicial volume and fillings of hyperbolic manifolds
Simplicial volume fillings of hyperbolic manifolds
2011/1/18
Let M be a hyperbolic n–manifold whose cusps have torus crosssections.In [FM10], the authors constructed a variety of nonpositively and negatively curved spaces as “2–fillings” of M by replacing the ...
An Alternative Presentation of the Symmetric-Simplicial Category
Alternative Presentation Symmetric-Simplicial Category
2011/1/19
t0, 1, . . . nuto include all functions between the same sets. Marco Grandis [Gra01a] has given a presentation of Fin using the standard generators di and si of Ord as well as the adjacent transpositi...
In [3] we have introduced the notion of covering projection on a general topos E. These are locally constant objects with an additional property.
Nonabelian Dold-Kan Decompositions for Simplicial and Symmetric-Simplicial Groups
Nonabelian Dold-Kan Decompositions Simplicial Symmetric-Simplicial Groups
2011/1/19
We extend the nonabelian Dold-Kan decomposition for simplicial groups of Carrasco and Cegarra [CC91] in two ways. First, we show that the total order of the subgroups in their decomposition belongs to...
Pseudo simplicial groups and crossed modules
Crossed modules Pseudo simplicial groups Moore complex
2010/12/20
In this paper, we define the notion of pseudo 2-crossed module and give a relation between the pseudo 2-crossed modules and pseudo simplicial groups with Moore complex of length 2.
Comparison of Cubical and Simplicial Derived Functors
Cubical Simplicial Derived Functors
2010/11/24
In this note we prove that the simplicial derived functors introduced by Tierney and Vogel [TV69] are naturally isomorphic to the cubical derived functors introduced by the author in [P09]. We also e...
Fibre sequences and localization of simplicial sheaves
Fibre sequences simplicial sheaves
2010/11/24
In this paper, we provide criteria for fibre sequences of simplicial sheaves to be preserved by nullification. This generalizes a result of Berrick and Dror Farjoun and allows a better understanding o...
An explicit description of the simplicial group $K(A,n)$
explicit description the simplicial group
2010/11/23
We give a new explicit construction for the simplicial group $K(A,n)$. We explain the topological interpretation and discuss some possible applications.