منابع مشابه
Cosmology, cohomology, and compactification
Ashtekar and Samuel have shown that Bianchi cosmological models with compact spatial sections must be of Bianchi class A. Motivated by general results on the symmetry reduction of variational principles, we show how to extend the Ashtekar-Samuel results to the setting of weakly locally homogeneous spaces as defined, e.g., by Singer and Thurston. In particular, it is shown that any mdimensional ...
متن کاملOn the Satake Isomorphism
In this paper, we present an expository treatment of the Satake transform. This gives an isomorphism between the spherical Hecke algebra of a split reductive group G over a local field and the representation ring of the dual group Ĝ. If one wants to use the Satake isomorphism to convert information on eigenvalues for the Hecke algebra to local L-functions, it has to be made quite explicit. This...
متن کاملOn the reductive Borel-Serre compactification: L p-cohomology of arithmetic groups (for large p)
Here, the left-hand side is the L-cohomology of M with respect to a (locally) invariant metric. Though it would be more natural to allow p = ∞ in Theorem 1, this is not generally possible (see (3.2.2)). On the other hand, there is a natural mapping H (∞)(M) → H • (p)(M) when p < ∞, because M has finite volume. The definition of M is recalled in (1.9). Theorem 1 can be viewed as an analogue of t...
متن کاملA generalization of the Kuga-Satake construction
The Kuga-Satake construction [3] associates to a polarized Hodge structure H of weight 2 with h2,0 = 1 an abelian variety A which satisfies the property that H is a sub-Hodge structure of Hom (H1(A),H1(A)). The construction is very tricky and intriguing geometrically: one first associates to the lattice (H,<,>) its Clifford algebra C(H), which is again a lattice. Then one constructs a complex s...
متن کاملKuga-satake Varieties and the Hodge Conjecture
Kuga-Satake varieties are abelian varieties associated to certain weight two Hodge structures, for example the second cohomology group of a K3 surface. We start with an introduction to Hodge structures and we give a detailed account of the construction of Kuga-Satake varieties. The Hodge conjecture is discussed in section 2. An excellent survey of the Hodge conjecture for abelian varieties is [...
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ژورنال
عنوان ژورنال: Topology
سال: 1983
ISSN: 0040-9383
DOI: 10.1016/0040-9383(83)90034-4