The index of projective families of elliptic operators.
The -groups of -rings. Part II. Invertibility of the logarithmic map
The Leibniz rule in algebraic -theory.
The Novikov conjecture for linear groups
Let K be a field. We show that every countable subgroup of GL(n,K) is uniformly embeddable in a Hilbert space. This implies that Novikov’s higher signature conjecture holds for these groups. We also show that every countable subgroup of GL(2,K) admits a proper, affine isometric action on a Hilbert space. This implies that the Baum-Connes conjecture holds for these groups. Finally, we show that every subgroup of GL(n,K) is exact, in the sense of C*-algebra theory.
The real K-ring of some CW-complexes of small dimension
The relative dihedral homology of involutive algebras.
The relative Riemann-Roch theorem from Hochschild homology.
The Roquette category of finite -groups
Let be a prime number. This paper introduces the Roquette category of finite -groups, which is an additive tensor category containing all finite -groups among its objects. In , every finite -group admits a canonical direct summand , called the edge of . Moreover splits uniquely as a direct sum of edges of Roquette -groups, and the tensor structure of can be described in terms of such edges. The main motivation for considering this category is that the additive functors from to...
The Schur multiplier of a generalized Baumslag-Solitar group
The signature package on Witt spaces
In this paper we prove a variety of results about the signature operator on Witt spaces. First, we give a parametrix construction for the signature operator on any compact, oriented, stratified pseudomanifold which satisfies the Witt condition. This construction, which is inductive over the ‘depth’ of the singularity, is then used to show that the signature operator is essentially self-adjoint and has discrete spectrum of finite multiplicity, so that its index—the analytic signature of —is well-defined....
The smooth Whitehead spectrum of a point at odd regular primes.
The spectral sequence relating algebraic K-theory to motivic cohomology
The structure of the tame kernels of quadratic number fields (II)
The structure of the tame kernels of quadratic number fields (I)
The surgery obstruction groups of the infinite dihedral group.
The symmetry of unit ideal stable range conditions
In this paper, we prove that unit ideal-stable range condition is right and left symmetric.
The syntomic regulator for the K-theory of fields
The tangent complex to the Bloch-Suslin complex
Motivated by a renewed interest for the “additive dilogarithm” appeared recently, the purpose of this paper is to complete calculations on the tangent complex to the Bloch-Suslin complex, initiated a long time ago and which were motivated at the time by scissors congruence of polyedra and homology of . The tangent complex to the trilogarithmic complex of Goncharov is also considered.
The Tate spectrum of vn-periodic complex oriented theories.
The torsion elements in K₂ of some local fields