256 citations · 944 across the 58 of their papers we have counts for
9 papers · 1 filter
The KO-valued spectral flow for skew-adjoint Fredholm operators
Chris Bourne, Alan L. Carey, Matthias Lesch +1
In this article we give a comprehensive treatment of a `Clifford module flow' along paths in the skew-adjoint Fredholm operators on a real Hilbert space that takes values in KO${}_…
The non-unital version of Connes' theorem on the Hochschild class of the Chern character
Alan L. Carey, A. Rennie
We offer a short proof of Connes' Hochschild class of the Chern character formula for non-unital semifinite spectral triples. The proof is simple due to its reliance on the authors…
Topological invariance of the homological index
Alan Carey, Jens Kaad
R. W. Carey and J. Pincus in [CaPi86] proposed and index theory for non-Fredholm bounded operators T on a separable Hilbert space H such that TT* - T*T is in the trace class. We sh…
Higher spectral flow and an entire bivariant JLO cocycle
Moulay-Tahar Benameur, Alan L. Carey
Given a smooth fibration of closed manifolds and a family of generalised Dirac operators along the fibers, we define an associated bivariant JLO cocycle. We then prove that, for an…
Riemann-Roch and index formulae in twisted K-theory
Alan L. Carey, Bai-Ling Wang
In this paper, we establish the Riemann-Roch theorem in twisted K-theory extending our earlier results. As an application, we prove a twisted index formula and show that D-brane ch…
Twisted cyclic theory and an index theory for the gauge invariant KMS state on Cuntz algebras
A. L. Carey, J. Phillips, A. Rennie
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 ho…
A noncommutative Atiyah-Patodi-Singer index theorem in KK-theory
A. L. Carey, J. Phillips, A. Rennie
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 r…
Thom isomorphism and Push-forward map in twisted K-theory
Alan L. Carey, Bai-Ling Wang
We establish the Thom isomorphism in twisted K-theory for any real vector bundle and develop the push-forward map in twisted K-theory for any differentiable proper map …
Spectral flow in Fredholm modules, eta invariants and the JLO cocycle
Alan L. Carey, John Phillips
We give a comprehensive account of an analytic approach to spectral flow along paths of self-adjoint Breuer-Fredholm operators in a type or von Neumann alg…