Related papers: Spectral morphisms, K-theory, and stable ranks
In this note we prove some results in flat and differential $K$-theory. The first one is a proof of the compatibility of the differential topological index and the flat topological index by a direct computation. The second one is the…
By introducing a notion of smooth connection for unbounded $KK$-cycles, we show that the Kasparov product of such cycles can be defined directly, by an algebraic formula. In order to achieve this it is necessary to develop a framework of…
We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting…
kk$^{\text{ban}}$ is a bivariant K-theory for Banach algebras that has reasonable homological properties, a product and is Morita invariant in a very general sense. We define it here by a universal property and ensure its existence in a…
The present paper explores substitution minimal systems and their relation to stationary Bratteli diagrams and stationary dimension groups. The constructions involved are algorithmic and explicit, and render an effective method to compute…
We study the spectral disjointness of the powers of a rank-one transformation. For a large class of rank-one constructions, including those for which the cutting and stacking parameters are bounded, and other examples such as rigid…
We construct a functional model for rank one perturbations of compact normal operators acting in a certain Hilbert spaces of entire functions generalizing de Branges spaces. Using this model we study completeness and spectral synthesis…
In this paper we introduce a spectra preserving relation between graphs with loops and graphs without loops. This relation is achieved in two steps. First, by generalizing spectra results got on (m, k)-stars to a wider class of graphs, the…
We investigate link homology theories for stable equivalence classes of link diagrams on orientable surfaces. We apply (1+1)-dimensional unoriented topological quantum field theories to Bar-Natan's geometric formalism to define new theories…
We show that after rationalization there is a homotopy fiber sequence BBU -> K(ku) -> K(Z). We interpret this as a correspondence between the virtual 2-vector bundles over a space X and their associated anomaly bundles over the free loop…
The paper deals with spectral order isomorphisms between certain spectral sublattices of direct sums of AW*-factors. We prove that these maps consist of spectral order isomorphisms between spectral sublattices of individual direct summands.…
We extend an example of B. Aupetit, which illustrates spectral discontinuity for operators on an infinite dimensional separable Hilbert space, to a general spectral discontinuity result in abstract Banach algebras. This can then be used to…
We use homotopy theoretic ideas to study the $K$-theory of (graded, Real) $C^*$-algebras in detail. After laying the foundations, and deriving the formal properties, the comparison of the model with the Kasparov picture of $K$-theory has…
Using principles of the theory of smoothness spaces we give systematic constructions of scales of inverse-closed subalgebras of a given Banach algebra with the action of a d-parameter automorphism group. In particular we obtain the…
We reveal a correspondence between the homological torsion of the Bianchi groups and new geometric invariants, which are effectively computable thanks to their action on hyperbolic space. We use it to explicitly compute their integral group…
Let $A \to B$ be a $G$-Galois extension of rings, or more generally of $\mathbb{E}_\infty$-ring spectra in the sense of Rognes. A basic question in algebraic $K$-theory asks how close the map $K(A) \to K(B)^{hG}$ is to being an equivalence,…
We study z-automorphisms of the polynomial algebra K[x,y,z] and the free associative algebra K<x,y,z> over a field K, i.e., automorphisms which fix the variable z. We survey some recent results on such automorphisms and on the corresponding…
Level-rank duality relates the observables of two different Chern-Simons theories in which the roles of the Chern-Simons level and the rank of the gauge group are exchanged. In this note, we explore the consequences of this duality in the…
The $k$-rank numerical range $\Lambda_{k}(A)$ is expressed via an intersection of a countable family of numerical ranges $\{F(M^{*}_{\nu}AM_{\nu})\}_{\nu\in\mathbb{N}}$ with respect to $n\times (n-k+1)$ isometries $M_{\nu}$. This…
Let $A$ and $B$ be unital semi-simple commutative Banach algebras. In this paper we study two-variable polynomials $p$ which satisfy the following property: a map $T$ from $A$ onto $B$ such that the equality \[ \sigma (p(Tf,Tg))=\sigma…