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1.
Following the introduction of an algebraic K-theory of special groups in [Dickmann and Miraglia, Algebra Colloq. 10 (2003) 149-176], generalizing Milnor's mod 2 K-theory for fields, the aim of this paper is to compute the K-theory of Boolean algebras, inductive limits, finite products, extensions, SG-sums and (finitely) filtered Boolean powers of special groups. A parallel theme is the preservation by these constructions of property [SMC], an analog for the K-theory of special groups of the property “multiplication by l(-1) is injective” in Milnor's mod 2 K-theory (see [Milnor, Invent. Math. 9 (1970) 318-344]).  相似文献   

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The Farrell-Jones Fibered Isomorphism Conjecture for the stable topological pseudoisotopy theory has been proved for several classes of groups. For example, for discrete subgroups of Lie groups [F.T. Farrell, L.E. Jones, Isomorphism conjectures in algebraic K-theory, J. Amer. Math. Soc. 6 (1993) 249-297], virtually poly-infinite cyclic groups [F.T. Farrell, L.E. Jones, Isomorphism conjectures in algebraic K-theory, J. Amer. Math. Soc. 6 (1993) 249-297], Artin braid groups [F.T. Farrell, S.K. Roushon, The Whitehead groups of braid groups vanish, Internat. Math. Res. Notices 10 (2000) 515-526], a class of virtually poly-surface groups [S.K. Roushon, The isomorphism conjecture for 3-manifold groups and K-theory of virtually poly-surface groups, math.KT/0408243, K-Theory, in press] and virtually solvable linear group [F.T. Farrell, P.A. Linnell, K-Theory of solvable groups, Proc. London Math. Soc. (3) 87 (2003) 309-336]. We extend these results in the sense that if G is a group from the above classes then we prove the conjecture for the wreath product G?H for H a finite group. The need for this kind of extension is already evident in [F.T. Farrell, S.K. Roushon, The Whitehead groups of braid groups vanish, Internat. Math. Res. Notices 10 (2000) 515-526; S.K. Roushon, The Farrell-Jones isomorphism conjecture for 3-manifold groups, math.KT/0405211, K-Theory, in press; S.K. Roushon, The isomorphism conjecture for 3-manifold groups and K-theory of virtually poly-surface groups, math.KT/0408243, K-Theory, in press]. We also prove the conjecture for some other classes of groups.  相似文献   

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In this paper we consider orders of images of nontorsion points by reduction maps for abelian varieties defined over number fields and for odd dimensional K-groups of number fields. As an application we obtain the generalization of the support problem for abelian varieties and K-groups.  相似文献   

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In the preceding papers [H. Hamanaka, A. Kono, On [X,U(n)], when dimX is 2n, J. Math. Kyoto Univ. 43 (2) (2003) 333-348; H. Hamanaka, On [X,U(n)], when dimX is 2n+1, J. Math. Kyoto Univ. 44 (3) (2004) 655-667; H. Hamanaka, Adams e-invariant, Toda bracket and [X,U(n)], J. Math. Kyoto Univ. 43 (4) (2003) 815-828], the group structure of the homotopy set [X,U(n)] with the pointwise multiplication is studied, where X is a finite CW-complex and U(n) is the unitary group. It is seen that nil[X,U(n)]=2 for some X with its dimension 2n, and, when dimX=2n+1 and n is even, [X,U(n)] is expressed as the two stage central extension of an Abelian group, i.e., nil[X,U(n)]?3.In this paper, we consider the nilpotency class of [X,U(n)], especially, for given k, the maximum of the nil[X,U(n)] under the condition dimX?2n+k is estimated and determined for k=0,1,2.  相似文献   

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In this paper, we develop twisted K-theory for stacks, where the twisted class is given by an S1-gerbe over the stack. General properties, including the Mayer-Vietoris property, Bott periodicity, and the product structure are derived. Our approach provides a uniform framework for studying various twisted K-theories including the usual twisted K-theory of topological spaces, twisted equivariant K-theory, and the twisted K-theory of orbifolds. We also present a Fredholm picture, and discuss the conditions under which twisted K-groups can be expressed by so-called “twisted vector bundles”.Our approach is to work on presentations of stacks, namely groupoids, and relies heavily on the machinery of K-theory (KK-theory) of C-algebras.  相似文献   

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Using an equivariant version of Connes? Thom isomorphism, we prove that equivariant K-theory is invariant under strict deformation quantization for a compact Lie group action.  相似文献   

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We define the new notion of R/Z-differential K-characters and study some properties. In particular, we show that the spectral eta invariant is an R/Z-secondary invariant in this theory.  相似文献   

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We prove the additivity theorem for the K-theory of triangulated derivators. This solves one of the conjectures made by Maltsiniotis in [G. Maltsiniotis, La K-théorie d'un dérivateur triangulé, in: Alexei Davydov, Michael Batanin, Michael Johnson, Stephen Lack, Amnon Neeman (Eds.), Categories in Algebra, Geometry and Physics, Conference and Workshop in honor of Ross Street's 60th Birthday, in: Contemp. Math., vol. 431, Amer. Math. Soc., 2007, pp. 341-368]. We also review some basic definitions and results in the theory of derivators in the sense of Grothendieck.  相似文献   

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We prove that the united K-theory functor is a surjective functor from the category of real simple separable purely infinite C-algebras to the category of countable acyclic CRT-modules. As a consequence, we show that every complex Kirchberg algebra satisfying the universal coefficient theorem is the complexification of a real C-algebra.  相似文献   

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Quantitative (or controlled) K-theory for C?-algebras was used by Guoliang Yu in his work on the Novikov conjecture, and later developed more formally by Yu together with Hervé Oyono-Oyono. In this paper, we extend their work by developing a framework of quantitative K-theory for the class of algebras of bounded linear operators on subquotients (i.e., subspaces of quotients) of Lp spaces. We also prove the existence of a controlled Mayer–Vietoris sequence in this framework.  相似文献   

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Marco Schlichting 《Topology》2004,43(5):1089-1103
We generalize, from additive categories to exact categories, the concept of “Karoubi filtration” and the associated homotopy fibration in algebraic K-theory. As an application, we construct for any idempotent complete exact category an exact category such that .  相似文献   

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Bertrand Toën 《Topology》2004,43(4):765-791
It is now well known that the K-theory of a Waldhausen category depends on more than just its (triangulated) homotopy category (Invent. Math. 150 (2002) 111). The purpose of this note is to show that the K-theory spectrum of a (good) Waldhausen category is completely determined by its Dwyer-Kan simplicial localization, without any additional structure. As the simplicial localization is a refined version of the homotopy category which also determines the triangulated structure, our result is a possible answer to the general question: “To which extent K-theory is not an invariant of triangulated derived categories? ”  相似文献   

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In [Amnon Neeman, Andrew Ranicki, Noncommutative localisation in algebraic K-theory I, Geom. Topol. 8 (2004) 1385-1425] we proved a localisation theorem in the algebraic K-theory of noncommutative rings. The main purpose of the current article is to express the general theorem of the previous paper in a more user-friendly fashion, in a way more suitable for applications. In the process we compare our result to the existing theorems in the literature, showing how the previous paper improves all the existing results.It should be pointed out that there have been two very interesting recent preprints on related topics. The reader is referred to the beautiful papers of Krause [Henning Krause, Cohomological quotients and smashing localizations, http://wwwmath.upb.de/~hkrause/publications.html. [8]] and Dwyer [William G. Dwyer, Noncommutative localization in homotopy theory, preprint, http://www.nd.edu/~wgd/. [4]]. Krause studies the lifting of chain complexes and the relation with the telescope conjecture, and Dwyer generalises to the homotopy theoretic framework.  相似文献   

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