Some algebraic aspects of quadratic forms over fields of characteristic two.
Splitting obstructions and properties of objects in the Nil categories
We show that the objects of Bass-Farrell categories which represent 0 in the corresponding Nil groups are precisely those which are stably triangular. This extends to Waldhausen's Nil group of the amalgamated free product with index 2 factors. Applications include a description of Cappell's special UNil group and reformulations of those splitting and fibering theorems which use the Nil groups.
Stable short exact sequences and the maximal exact structure of an additive category
It was recently proved that every additive category has a unique maximal exact structure, while it remained open whether the distinguished short exact sequences of this canonical exact structure coincide with the stable short exact sequences. The question is answered by a counterexample which shows that none of the steps to construct the maximal exact structure can be dropped.
Strictification of categories weakly enriched in symmetric monoidal categories.
Symbol lengths in Milnor -theory.
Symmetric monoidal categories model all connective spectra.
The 4-rank of the tame kernel versus the 4-rank of the narrow class group in quadratic number fields
The additivity theorem in algebraic -theory.
The boundary of the Eisenstein symbol.
The boundary of the Eisenstein symbol (Erratum).
The Brauer and Brauer-Taylor groups of a symmetric monoidal category
The connection between the -theory localization theorem of Thomason, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel
The cyclotomic trace and algebraic K-theory of spaces.
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 indecomposable of fields
The relative dihedral homology of involutive algebras.
The smooth Whitehead spectrum of a point at odd regular primes.
Topological -theory of the integers at the prime 2.