• Corpus ID: 55940445

Poincare duality for Cuntz-Pimsner algebras of bimodules

@article{Rennie2018PoincareDF,
  title={Poincare duality for Cuntz-Pimsner algebras of bimodules},
  author={Adam Graham Rennie and David Robertson and Aidan Sims},
  journal={arXiv: K-Theory and Homology},
  year={2018}
}
We present a new approach to Poincare duality for Cuntz-Pimsner algebras. We provide sufficient conditions under which Poincare self-duality for the coefficient algebra of a Hilbert bimodule lifts to Poincare self-duality for the associated Cuntz-Pimsner algebra. With these conditions in hand, we can constructively produce fundamental classes in K-theory for a wide range of examples. We can also produce K-homology fundamental classes for the important examples of Cuntz-Krieger algebras… 

A geometric representative for the fundamental class in KK-duality of Smale spaces

. A fundamental ingredient in the noncommutative geometry program is the notion of KK-duality, often called K-theoretic Poincar´e duality, that generalises Spanier-Whitehead duality. In this paper we

Higher-rank graph algebras are iterated Cuntz-Pimsner algebras

Given a finitely aligned $k$-graph $\Lambda$, we let $\Lambda^i$ denote the $(k-1)$-graph formed by removing all edges of degree $e_i$ from $\Lambda$. We show that the Toeplitz-Cuntz-Krieger algebra

References

SHOWING 1-10 OF 38 REFERENCES

The extension class and KMS states for Cuntz--Pimsner algebras of some bi-Hilbertian bimodules

For bi-Hilbertian $A$-bimodules, in the sense of Kajiwara--Pinzari--Watatani, we construct a Kasparov module representing the extension class defining the Cuntz--Pimsner algebra. The construction

Twisted cyclic theory, equivariant KK-theory and KMS states

Abstract Given a C*-algebra A with a KMS weight for a circle action, we construct and compute a secondary invariant on the equivariant K-theory of the mapping cone of , both in terms of equivariant

K-Theoretic Duality for Shifts of Finite Type

Abstract:We will study the stable and unstable Ruelle algebras associated to a hyperbolic homeomorphism of a compact space. To do this, we will describe a notion of K-theoretic duality for -algebras

Shift–tail equivalence and an unbounded representative of the Cuntz–Pimsner extension

We show how the fine structure in shift–tail equivalence, appearing in the non-commutative geometry of Cuntz–Krieger algebras developed by the first two listed authors, has an analogue in a wide

Noncommutative Atiyah-Patodi-Singer boundary conditions and index pairings in KK-theory

Abstract We investigate an extension of ideas of Atiyah-Patodi-Singer (APS) to a noncommutative geometry setting framed in terms of Kasparov modules. We use a mapping cone construction to relate odd

Smoothness and Locality for Nonunital Spectral Triples

To deal with technical issues in noncommutative geometry for nonunital algebras, we introduce a useful class of algebras and their modules. These algebras and modules allow us to extend all of the

Spanier–Whitehead K-duality for C∗-algebras

Classical Spanier–Whitehead duality was introduced for the stable homotopy category of finite CW complexes. Here we provide a comprehensive treatment of a noncommutative version, termed

Wieler solenoids, Cuntz–Pimsner algebras and $K$ -theory

We study irreducible Smale spaces with totally disconnected stable sets and their associated $K$ -theoretic invariants. Such Smale spaces arise as Wieler solenoids, and we restrict to those arising

Modular spectral triples and KMS states in noncommutative geometry

This thesis investigates the role of dimension in the noncommutative geometry of quantum groups and their homogeneous spaces. We define a generahsation of semifinite spectral triples called modular

D-Branes, RR-Fields and Duality on Noncommutative Manifolds

We develop some of the ingredients needed for string theory on noncommutative spacetimes, proposing an axiomatic formulation of T-duality as well as establishing a very general formula for D-brane