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1.
We show that the Atiyah–Hirzebruch K-theory of spaces admits a canonical generalization for stratified spaces. For this we study algebraic constructions on stratified vector bundles. In particular the tangent bundle of a stratified manifold is such a stratified vector bundle. 相似文献
2.
Algebraic K-Theory and the Conjectural Leibniz K-Theory 总被引:1,自引:0,他引:1
Jean-Louis Loday 《K-Theory》2003,30(2):105-127
The analogy between algebraic K-theory and cyclic homology is used to build a program aiming at understanding the algebraic K-theory of fields and the periodicity phenomena in algebraic K-theory. In particular, we conjecture the existence of a Leibniz K-theory which would play the role of Hochschild homology. We propose a motivated presentation for the Leibniz K
2-group ofa field. 相似文献
3.
Kimberly Pearson 《K-Theory》1998,14(3):265-280
Abstract. We explicitly compute the lower algebraicK-groups of the two-dimensional crystallographic groups. 相似文献
4.
If X is a smooth curve defined over the real numbers , we show that K
n
(X) is the sum of a divisible group and a finite elementary Abelian 2-group when n 2. We determine the torsion subgroup of K
n
(X), which is a finite sum of copies of and 2, only depending on the topological invariants of X() and X(), and show that (for n 2) these torsion subgroups are periodic of order 8. 相似文献
5.
We prove that for smooth surfaces over real closed fields, and a class of smooth projective surfaces over a real number field, the map between mod 2 algebraic and étale K-theory is an isomorphism in sufficiently large degrees. For a class of smooth projective surfaces over a real closed field, including rational surfaces, complete intersections and K3-surfaces over the real numbers, we explicate the abutment of the mod 2 motivic cohomology to algebraic K-theory spectral sequence. 相似文献
6.
We use a Heegaard splitting of the topological 3-sphere as a guiding principle to construct a family of its noncommutative
deformations. The main technical point is an identification of the universal C*-algebras defining our quantum 3-spheres with an appropriate fiber product of crossed-product C*-algebras. Then we employ this result to show that the K-groups of our family of noncommutative 3-spheres coincide with their classical counterparts.
Dedicated to the memory of Olaf Richter
An erratum to this article is available at . 相似文献
7.
Stephen A. Mitchell 《K-Theory》2002,25(1):1-37
We explicitly determine the homotopy type of the 2-completed algebraic K-theory spectrum KF, where F is an arbitrary finite extension of the 2-adic rational numbers. The answer is formulated in terms of topological complex K-theory and the K-theory of suitable finite fields, suspended copies of which are glued together by connecting maps that depend on the Iwasawa theory of F. 相似文献
8.
We describe Bott towers as sequences of toric manifolds Mk, and identify the omniorientations which correspond to their original construction as complex varieties. We show that the suspension of Mk is homotopy equivalent to a wedge of Thom complexes, and display its complex K-theory as an algebra over the coefficient ring. We extend the results to KO-theory for several families of examples, and compute the effects of the realification homomorphism; these calculations breathe geometric life into Bahri and Benderskys analysis of the Adams Spectral Sequence [Bahri, A. and Bendersky, M.: The KO-theory of toric manifolds. Trans. Am. Math. Soc. 352 (2000), 1191–1202.] By way of application we consider the enumeration of stably complex structures on Mk, obtaining estimates for those which arise from omniorientations and those which are almost complex. We conclude with observations on the rôle of Bott towers in complex cobordism theory.Mathematics Subject Classification (2000): 55R25, 55R50, 57R77.(Received: August 2004) 相似文献
9.
《K-Theory》2006,37(1-2):25-104
A families index theorem in K-theory is given for the setting of Atiyah, Patodi, and Singer of a family of Dirac operators with spectral boundary condition.
This result is deduced from such a K-theory index theorem for the calculus of cusp, or more generally fibred-cusp, pseudodifferential operators on the fibres
(with boundary) of a fibration; a version of Poincaré duality is also shown in this setting, identifying the stable Fredholm
families with elements of a bivariant K-group.
(Received: February 2006) 相似文献
10.
We show that the Fibered Isomorphism Conjecture of T. Farrell and L. Jones holds for various mapping class groups. In many cases, we explicitly calculate the lower algebraic K-groups, showing that they do not always vanish. 相似文献
11.
Tyler Lawson 《K-Theory》2006,37(4):395-422
For finitely generated groups G and H, we prove that there is a weak equivalence
G H (G × H) of ku-algebra spectra, where denotes the “unitary deformation K-theory” functor. Additionally, we give spectral sequences for computing the homotopy groups of G and HG in terms of connective K-theory and homology of spaces of G-representations. 相似文献
12.
Wojciech Dorabiaa 《K-Theory》2002,25(3):251-276
The goal of this paper is to show that if a smooth fiber bundle has a compact Lie group as a structure group, then the transfer map for the algebraic K-theory of spaces satisfies analogs of the Mackey double coset formula and Feshbach's sum formula. We also prove a cut and paste formula for parametrized Reidemeister torsion. 相似文献
13.
Joseph Gubeladze 《K-Theory》2003,28(4):285-327
A natural higher K-theoretic analogue of the triviality of vector bundles on affine toric varieties is the conjecture on nilpotence of the multiplicative action of the natural numbers on the K-theory of these varieties. This includes both Quillen's fundamental result on K-homotopy invariance of regular rings and the stable version of the triviality of vector bundles on affine toric varieties. Moreover, it yields a similar behavior of not necessarily affine toric varieties and, further, of their equivariant closed subsets. The conjecture is equivalent to the claim that the relevant admissible morphisms of the category of vector bundles on an affine toric variety can be supported by monomials not in a nondegenerate corner subcone of the underlying polyhedral cone. We prove that one can in fact eliminate all lattice points in such a subcone, except maybe one point. The elimination of the last point is also possible in 0 characteristic if the action of the big Witt vectors satisfies a very natural condition. A partial result of this in the arithmetic case provides first nonsimplicial examples, actually an explicit infinite series of combinatorially different affine toric varieties, simultaneously verifying the conjecture for all higher groups.Supported by the Deutsche Forschungsgemeinschaft, INTAS grant 99-00817 and TMR grant ERB FMRX CT-97-0107 相似文献
14.
It is proved that algebraic and topological K-functors are isomorphic on the category of stable generalized operator algebras which are K
i
-regular for all i > 0. 相似文献
15.
Andrew J. Nicas 《K-Theory》1987,1(5):437-456
Deligne defined the notion of a mixed Hodge structure (MHS) and proved that every quasiprojective variety over has a natural MHS on its cohomology. This paper establishes similar results for cyclic homology and the algebraic K-theory of simply connected quasi-projective varieties over . In the nonsimply connected case, an MHS is established on certain quotient groups of algebraic K-theory.Supported by a NSERC University Research Fellowship and operating grant. 相似文献
16.
Yongjin Song 《K-Theory》1991,5(6):485-501
We define the Volodin hermitian algebraic K-theory for a (discrete) ring with an involution and show that it is isomorphic to Karoubi's hermitian algebraic K-theory. We also construct the Volodin model
X(R
*) of hermitian algebraic K-theory for a simplicial ring R
* and show that it is a homotopy fiber of the map B
Ô(R
*)B
Ô(R
*)+. We also prove the general linear version of this result, which has been claimed in the existing literature, but whose proof was overlooked. 相似文献
17.
Mark E. Walker 《K-Theory》2002,26(3):207-286
In this paper, we introduce the 'semi-topological K-homology' of complex varieties, a theory related to semi-topological K-theory much as connective topological K-homology is related to connective topological K-theory. Our main theorem is that the semi-topological K-homology of a smooth, quasi-projective complex variety Y coincides with the connective topological K-homology of the associated analytic space Y
an. From this result, we deduce a pair of results relating semi-topological K-theory with connective topological K-theory. In particular, we prove that the 'Bott inverted' semi-topological K-theory of a smooth, projective complex variety X coincides with the topological K-theory of X
an. In combination with a result of Friedlander and the author, this gives a new proof, in the special case of smooth, projective complex varieties, of Thomason's celebrated theorem that 'Bott inverted' algebraic K-theory with /n coefficients coincides with topological K-theory with /n coefficients. 相似文献
18.
Hanfeng Li 《K-Theory》2004,32(4):323-329
We construct examples of flabby strict deformation quantizations not preserving K-groups. This answers a question of Rieffel negatively. 相似文献
19.
We give a closed formula for topological K-theory of the homogeneous space N/, where is the standard integer lattice in the simply connected Heisenberg Lie group N of dimension 2n+1, n
. The main tools in our calculations are obtained by computing diagonal forms for certain incidence matrices that arise naturally in combinatorics. 相似文献
20.
Kei Hagihara 《K-Theory》2003,29(2):75-99
In this paper we develop a K-theory of log schemes by using vector bundles on the Ket site. Then, for a wide class of log varieties, we describe the structure of their K-groups in terms of the usual algebraic K-groups. 相似文献