The cyclotomic trace and algebraic K-theory of spaces.
The equivariant -homomorphism.
The existence of higher logarithms
The Gersten conjecture for Witt groups in the equicharacteristic case.
The Grothendieck group of GL(F)×GL(G)-equivariant modules over the coordinate ring of determinantal varieties
The Grothendieck-Riemann-Roch theorem for group scheme actions
The Hatcher-Waldhausen map is a spectrum map.
The Hochschild cohomology of a closed manifold
Let M be a closed orientable manifold of dimension dand be the usual cochain algebra on M with coefficients in a fieldk. The Hochschild cohomology of M, is a graded commutative and associative algebra. The augmentation map induces a morphism of algebras . In this paper we produce a chain model for the morphism I. We show that the kernel of I is a nilpotent ideal and that the image of I is contained in the center of , which is in general quite small. The algebra is expected to be isomorphic...
The homology of special linear groups over polynomial rings
The image of the natural homomorphism of Witt rings of orders in a global field
Let R be a Dedekind domain whose field of fractions is a global field. Moreover, let 𝓞 < R be an order. We examine the image of the natural homomorphism φ : W𝓞 → WR of the corresponding Witt rings. We formulate necessary and sufficient conditions for the surjectivity of φ in the case of all nonreal quadratic number fields, all real quadratic number fields K such that -1 is a norm in the extension K/ℚ, and all quadratic function fields.
The indecomposable of fields
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