We characterize exchange rings having stable range one. An exchange ring has stable range one if and only if for any regular , there exist an and a such that and if and only if for any regular , there exist and such that if and only if for any , .
We prove that entire and periodic cyclic cohomology satisfy excision for extensions of bornological algebras with a bounded linear section. That is, for such an extension we obtain a six term exact sequence in cohomology.
The product of two Schubert classes in the quantum -theory ring of a homogeneous space is a formal power series with coefficients in the Grothendieck ring of algebraic vector bundles on . We show that if is cominuscule, then this power series has only finitely many non-zero terms. The proof is based on a geometric study of boundary Gromov-Witten varieties in the Kontsevich moduli space, consisting of stable maps to that take the marked points to general Schubert varieties and whose domains...
The relationship between fixed point theory and K-theory is explained, both classical Nielsen theory (versus ) and 1-parameter fixed point theory (versus ). In particular, various zeta functions associated with suspension flows are shown to come in a natural way as “traces” of “torsions” of Whitehead and Reidemeister type.
Let be a compact Lie group acting in a Hamiltonian way on a symplectic manifold which is pre-quantized by a Kostant-Souriau line bundle. We suppose here that the moment map is proper so that the reduced space is compact for all . Then, we can define the “formal geometric quantization” of asThe aim of this article is to study the functorial properties of the assignment .
Introduite par Witt en 1937, la théorie des formes quadratiques sur un corps joue un rôle central dans la démonstration des conjectures de Milnor par Voevodsky via les travaux pionniers de Rost qui y interviennent. Réciproquement, les méthodes de Rost et Voevodsky utilisant la théorie des motifs et les opérations de Steenrod motiviques révolutionnent la théorie des formes quadratiques et ont conduit à la démonstration de résultats de base qui semblaient auparavant inaccessibles. On expliquera notamment...
Dans cet article on donne une formule explicite pour le caractère de Chern reliant la - théorie algébrique et l’homologie cyclique négative. On calcule le caractère de Chern des symboles de Steinberg et de Loday et on donne une preuve élémentaire du fait que le caractère de Chern est multiplicatif.