Compactly supported cohomology of buildings
نویسندگان
چکیده
Suppose (W,S) is a Coxeter system. A subset T ⊂ S is spherical if it generates a finite subgroup of W . S denotes the poset of spherical subsets of S. Let Φ be a building in the sense of [6] (i.e., Φ is a set of chambers, equipped with a family of adjacency relations indexed by S and a W -valued distance function, Φ×Φ→W ). Let A denote the set of finitely supported Z-valued functions on Φ (i.e., A is the free abelian group on Φ). For each T ∈ S, A denotes the set of f ∈ A which are constant on all residues of type T . If U ⊃ T , then A ⊂ T . We show that the quotient, D := A / ∑ s∈S−T A T∪{s}, is free abelian. Let  be a summand of A which projects isomorphically onto D . Decomposition Theorem. For each T ∈ S, A = ⊕
منابع مشابه
ar X iv : 0 80 6 . 24 12 v 1 [ m at h . G R ] 1 5 Ju n 20 08 Compactly supported cohomology of buildings
We compute the compactly supported cohomology of the standard realization of any locally finite building. AMS classification numbers. Primary: 20F65 Secondary: 20E42, 20F55, 20J06, 57M07.
متن کاملThe Penrose transform for compactly supported cohomology
Let the manifold X parametrise a family of compact complex submanifolds of the complex (or CR) manifold Z. Under mild conditions the Penrose transform typically provides isomorphisms between a cohomology group of a holomorphic vector bundle V → Z and the kernel of a differential operator between sections of vector bundles over X. When the spaces in question are homogeneous for a group G the Pen...
متن کاملCollocation Method using Compactly Supported Radial Basis Function for Solving Volterra's Population Model
In this paper, indirect collocation approach based on compactly supported radial basis function (CSRBF) is applied for solving Volterra's population model. The method reduces the solution of this problem to the solution of a system of algebraic equations. Volterra's model is a non-linear integro-differential equation where the integral term represents the effect of toxin. To solve the pr...
متن کاملThe Smooth Cohomology of N=2 Supersymmetric Landau-ginzburg Eld Theories
We compute the smooth cohomology (both unrestricted and compactly supported) of the supercharge of an ultraviolet cutoo N = 2 supersymmetric Landau-Ginzburg eld theory.
متن کاملC P . D N
We begin by introducing some notation and definitions to get our investigation of compactly supported cohomolgy started. We then proceed to compute the compactly supported cohomology groups of simple spaces like ∗ = R, R and R. From these special cases, we will see how to generalize the computation to R. ereaer, we will prove the general version of the Poincaré Lemma, whi states H• c (M × R)...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008