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Twisted K-Theory and K-Theory of Bundle Gerbes
Abstract: In this note we introduce the notion of bundle gerbe K-theory and investigate the relation to twisted K-theory. We provide some examples. Possible applications of bundle gerbe K-theory toExpand
On fermion gauge groups, current algebras and Kac-Moody algebras
Representations of groups of loops in U(N), SO(N) and various subgroups are studied. The representations are defined on fermion Fock spaces, and may be regarded as local gauge groups in the contextExpand
Spectral flow and Dixmier traces
Abstract We obtain general theorems which enable the calculation of the Dixmier trace in terms of the asymptotics of the zeta function and of the heat operator in a general semi-finite von NeumannExpand
Thom isomorphism and push-forward map in twisted K-theory
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 $f: X\to Y$ (not necessarilyExpand
Index Theory for Locally Compact Noncommutative Geometries
Introduction Pseudodifferential calculus and summability Index pairings for semifinite spectral triples The local index formula for semifinite spectral triples Applications to index theorems on openExpand
Spectral flow in Fredholm modules, eta invariants and the JLO cocycle
We give a comprehensive account of an analytic approach to spectral flow along paths of self-adjoint Breuer-Fredholm operators in a type $I_{\infty}$ or $II_\infty$ von Neumann algebra ${\mathcalExpand
Holonomy on D-branes
Abstract This paper shows how to construct anomaly free world sheet actions in string theory with D-branes. Our method is to use Deligne cohomology and bundle gerbe theory to define geometric objectsExpand
The Dixmier trace and asymptotics of zeta functions
Abstract We obtain general theorems which enable the calculation of the Dixmier trace in terms of the asymptotics of the zeta function and of the trace of the heat semigroup. We prove our results inExpand
Quantum Hall Effect on the Hyperbolic Plane
Abstract:In this paper, we study both the continuous model and the discrete model of the Quantum Hall Effect (QHE) on the hyperbolic plane. The Hall conductivity is identified as a geometricExpand
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