Page 1 WINFRIED BRUNS JOSEPH GUBELADZE Polytopes, Rings, and K-Theory Springer
Springer Monographs in Mathematics Page 2 Springer Monographs in Mathematics For further …

High-dimensional knot theory is the study of the embeddings of n-dimensional manifolds in
(n+ 2)-dimensional manifolds, generalizing the traditional study of knots in the case n= 1 …

Twenty years ago Bloch,[B1], introduced the complex C.(A; p) of p-typical curves in K-theory
and outlined its connection to the crystalline cohomology of Berthelot-Grothendieck …

We present the status of the Farrell–Jones Conjecture for algebraic K-theory for a group G
and arbitrary coefficient rings R. We add new groups for which the conjecture is known to be …

We show that there is a natural decomposition Pic (A t, t^-1) ≅ Pic (A) ⊕ NPic (A) ⊕ NPic (A)
⊕ H^ 1 (A) for any commutative ring A, where Pic (A) is the Picard group of invertible A …

If A is an affine algebra of dimension d≥ 2, over a perfect field k, where char k= 2 and cd 2
k≤ 1, or if A= R [X], where R is a local, noetherian ring of dimension d≥ 2, in which 2R= R …

We investigate the relative assembly map from the family of finite subgroups to the family of
virtually cyclic subgroups for the algebraic K-theory of twisted group rings of a group G with …

Let R be a commutative ring, A= A 0⊕ A 1⊕… a graded R-algebra, and A+ the graded ideal
A 1⊕ A 2⊕… Then K i (A)= K i (A 0)⊕ K i (A, A+). We show that the groups K i (A, A+) are …

We extend the $ K $-theory of endomorphisms functor from ordinary rings to (stable) $\infty $-
categories. We show that $\mathrm {KEnd}(-) $ descends to the category of noncommutative …

For every mathematician, ring theory and K-theory are intimately connected: algebraic K-
theory is largely the K-theory of rings. At first sight, polytopes, by their very nature, must …