相关论文: Type III and spectral triples
In order to treat multiplicative phenomena in twisted (co)homology, we introduce a new point-set level framework for parametrized homotopy theory. We provide a convolution smash product that descends to the corresponding…
The construction of twisted K-theory classes on a compact Lie group is reviewed using the supersymmetric Wess-Zumino-Witten model on a cylinder. The Quillen superconnection is introduced for a family of supercharges and the Chern character…
In this article, we further the study of higher K-theory of dg categories via universal invariants, initiated by the second named author. Our main result is the co-representability of non-connective K-theory by the base ring in the…
Recently, examples of an index theory for KMS states of circle actions were discovered, \cite{CPR2,CRT}. We show that these examples are not isolated. Rather there is a general framework in which we use KMS states for circle actions on a…
We review the recent construction of semifinite spectral triples for graph C^*-algebras. These examples have inspired many other developments and we review some of these such as the relation between the semifinite index and the Kasparov…
We systematically investigate ways to twist a real spectral triple via an algebra automorphism and in particular, we naturally define a twisted partner for any real graded spectral triple. Among other things we investigate consequences of…
Given a henselian pair $(R, I)$ of commutative rings, we show that the relative $K$-theory and relative topological cyclic homology with finite coefficients are identified via the cyclotomic trace $K \to \mathrm{TC}$. This yields a…
In order to study continuous models of disordered topological phases, we construct an unbounded Kasparov module and a semifinite spectral triple for the crossed product of a separable $C^*$-algebra by a twisted $\mathbb{R}^d$-action. The…
The purpose of this paper is to show the relationship in all dimensions between the structural (diffraction pattern) aspect of tilings (described by \v{C}ech cohomology of the tiling space) and the spectral properties (of Hamiltonians…
Making use of the theory of noncommutative motives, we characterize the topological Dennis trace map as the unique multiplicative natural transformation from algebraic K-theory to topological Hochschild homology (THH) and the cyclotomic…
We define pseudo-Riemannian spectral triples, an analytic context broad enough to encompass a spectral description of a wide class of pseudo-Riemannian manifolds, as well as their noncommutative generalisations. Our main theorem shows that…
This is the second paper in a series of three papers aiming to study cohomology of group theoretic Dehn fillings. In the present paper, we derive a spectral sequence for Cohen-Lyndon triples which can be thought of as a refined version of…
We provide a formula for the Chern character of a holomorphic vector bundle in the hyper-cohomology of the de Rham complex of holomorphic sheaves on a complex manifold. This Chern character can be thought of as a completion of the Chern…
This paper expresses the Chern character for topological K-theory based on the formulation of the family of Fredholm operators, by using the points at which the Fredholm operator becomes singular (Fermi points). In particular, we explain…
This paper presents, by example, an index theory appropriate to algebras without trace. Whilst we work exclusively with the Cuntz algebras the exposition is designed to indicate how to develop a general theory. Our main result is an index…
We consider surfaces of geometric genus $3$ with the property that their transcendental cohomology splits into $3$ pieces, each piece coming from a $K3$ surface. For certain families of surfaces with this property, we can show there is a…
Over an algebraically closed ffeld F of characteristic p>0, the restricted twisted Heisenberg Lie algebras are studied. We use the Hochschild-Serre spectral sequence relative to its Heisenberg ideal to compute the trivial cohomology. The…
The purpose of this work is to provide details about the construction of the Chern character for categorical sheaves mentioned in our previous work "Chern character, loop spaces and derived algebraic geometry". For this, we introduce and…
In order to study the Hochschild cohomology of triangular algebras $\mathcal T$, we construct a spectral sequence, whose terms are parametrized by the length of the trajectories of the quiver associated with $\mathcal T$, and which…
This paper investigates a variety of coarse homology theories and natural transformations between them. We in particular study the commutativity of a square relating analytical and topological transgressions with algebraic and homotopy…