Cyclic Cohomology, Supersymmetry and KMS States The KMS States as Generalized Elliptic Operators
Decompositions of the category of noncommutative sets and Hochschild and cyclic homology
In this note we show that the main results of the paper [PR] can be obtained as consequences of more general results concerning categories whose morphisms can be uniquely presented as compositions of morphisms of their two subcategories with the same objects. First we will prove these general results and then we will apply it to the case of finite noncommutative sets.
Differentials in the homological homotopy fixed point spectral sequence.
Dilogarithm, grassmannian complex and scissors congruence groups of algebraic polyhedra
Divisibility of the Dirac magnetic monopole as a two-vector bundle over the three-sphere.
Dualization in algebraic K-theory and the invariant e¹ of quadratic forms over schemes
In the classical Witt theory over a field F, the study of quadratic forms begins with two simple invariants: the dimension of a form modulo 2, called the dimension index and denoted e⁰: W(F) → ℤ/2, and the discriminant e¹ with values in k₁(F) = F*/F*², which behaves well on the fundamental ideal I(F)= ker(e⁰). Here a more sophisticated situation is considered, of quadratic forms over a scheme and, more generally, over an exact category with duality. Our purposes are: ...
Equivariant cyclic homology and equivariant differential forms
Equivariant higher algebraic K-theory for Waldhausen categories.
Equivariant higher -theory for compact Lie group actions.
Equivariant local cyclic homology and the equivariant Chern-Connes character.
Étale descent for Hochschild and cyclic homology.
Excision en -théorie algébrique
Excision in entire cyclic cohomology
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.
Extension categories and their homotopy
Fibrant presheaves of spectra and Guillén-Navarro extension
Filtered topological cyclic homology and relative -theory of nilpotent ideals.
Fixed point theory and the K-theoretic trace
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.
Fonctions polylogarithmes, nombres polyzêtas et groupes pro-unipotents
Formules explicites pour le caractère de Chern en -théorie algébrique
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.
Galois module structure of Milnor -theory in characteristic .