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138
Twisted Ktheory of differentiable stacks
 ANN. SCI. ÉCOLE NORM. SUP
, 2004
"... In this paper, we develop twisted Ktheory for stacks, where the twisted class is given by an S 1gerbe over the stack. General properties, including the Mayer–Vietoris property, Bott periodicity, and the product structure K i α ⊗K j β → Ki+j α+β are derived. Our approach provides a uniform framew ..."
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Cited by 75 (13 self)
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In this paper, we develop twisted Ktheory for stacks, where the twisted class is given by an S 1gerbe over the stack. General properties, including the Mayer–Vietoris property, Bott periodicity, and the product structure K i α ⊗K j β → Ki+j α+β are derived. Our approach provides a uniform framework for studying various twisted Ktheories including the usual twisted Ktheory of topological spaces, twisted equivariant Ktheory, and the twisted Ktheory of orbifolds. We also present a Fredholm picture, and discuss the conditions under which twisted Kgroups can be expressed by socalled “twisted vector bundles”. Our approach is to work on presentations of stacks, namely groupoids, and relies heavily on the machinery of Ktheory (KKtheory) of C ∗algebras.
Twisted equivariant Ktheory with complex coefficients
, 2008
"... Using a global version of the equivariant Chern character, we describe an effective method for computing the complexified twisted equivariant Ktheory of a space ..."
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Cited by 70 (7 self)
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Using a global version of the equivariant Chern character, we describe an effective method for computing the complexified twisted equivariant Ktheory of a space
Bundle Gerbes for ChernSimons and WESSZUMINOWITTEN THEORIES
, 2005
"... We develop the theory of ChernSimons bundle 2gerbes and multiplicative bundle gerbes associated to any principal Gbundle with connection and a class in H4 (BG, Z) for a compact semisimple Lie group G. The ChernSimons bundle 2gerbe realises differential geometrically the CheegerSimons invarian ..."
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Cited by 48 (9 self)
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We develop the theory of ChernSimons bundle 2gerbes and multiplicative bundle gerbes associated to any principal Gbundle with connection and a class in H4 (BG, Z) for a compact semisimple Lie group G. The ChernSimons bundle 2gerbe realises differential geometrically the CheegerSimons invariant. We apply these notions to refine the DijkgraafWitten correspondence between three dimensional ChernSimons functionals and WessZuminoWitten models associated to the group G. We do this by introducing a lifting to the level of bundle gerbes of the natural map from H 4 (BG, Z) to H3 (G, Z). The notion of a multiplicative bundle gerbe accounts geometrically for the subtleties in this correspondence for nonsimply connected Lie groups. The implications for WessZuminoWitten models are also discussed.
Thom isomorphism and Pushforward map in twisted Ktheory
"... Abstract. We establish the Thom isomorphism in twisted Ktheory for any real vector bundle and develop the pushforward map in twisted Ktheory for any differentiable proper map f: X → Y (not necessarily Koriented). The pushforward map generalizes the pushforward map in ordinary Ktheory for any K ..."
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Cited by 38 (5 self)
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Abstract. We establish the Thom isomorphism in twisted Ktheory for any real vector bundle and develop the pushforward map in twisted Ktheory for any differentiable proper map f: X → Y (not necessarily Koriented). The pushforward map generalizes the pushforward map in ordinary Ktheory for any Koriented differentiable proper map and the AtiyahSinger index theorem of Dirac operators on Clifford modules. For Dbranes satisfying FreedWitten’s anomaly cancellation condition in a manifold with a nontrivial Bfield, we associate a canonical element in the twisted Kgroup to get the socalled Dbrane charges. Contents
Nonabelian Bundle Gerbes, their Differential Geometry and Gauge Theory
, 2003
"... Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studied both in a global coordinate independent formalism and in local coordinates. These are the gauge field ..."
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Cited by 36 (3 self)
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Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studied both in a global coordinate independent formalism and in local coordinates. These are the gauge fields needed for the construction of YangMills theories with 2form gauge potential.
Holonomy on Dbranes
 J. Geom. Phys
"... Abstract. This paper shows how to construct anomaly free world sheet actions in string theory with Dbranes. Our method is to use Deligne cohomology and bundle gerbe theory to define geometric objects which are naturally associated to Dbranes and connections on them. The holonomy of these connectio ..."
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Cited by 34 (2 self)
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Abstract. This paper shows how to construct anomaly free world sheet actions in string theory with Dbranes. Our method is to use Deligne cohomology and bundle gerbe theory to define geometric objects which are naturally associated to Dbranes and connections on them. The holonomy of these connections can be used to cancel global anomalies in the world sheet action. 1.
Gerbes, M5Brane Anomalies and E8 Gauge Theory
, 2004
"... Abelian gerbes and twisted bundles describe the topology of the NS 3form gauge field strength H. We review how they have been usefully applied to study and resolve global anomalies in open string theory. Abelian 2gerbes and twisted nonabelian gerbes describe the topology of the 4form field streng ..."
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Cited by 29 (0 self)
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Abelian gerbes and twisted bundles describe the topology of the NS 3form gauge field strength H. We review how they have been usefully applied to study and resolve global anomalies in open string theory. Abelian 2gerbes and twisted nonabelian gerbes describe the topology of the 4form field strength G of Mtheory. We show that twisted nonabelian gerbes are relevant in the study and resolution of global anomalies of multiple coinciding M5branes. Global anomalies for one M5brane have been studied by Witten and by Diaconescu, Freed and Moore. The structure and the differential geometry of twisted nonabelian gerbes (i.e. modules for 2gerbes) is defined and studied. The nonabelian 2form gauge potential living on multiple coinciding M5branes arises as curving (curvature) of twisted nonabelian gerbes. The nonabelian group is in general ˜ ΩE8, the central extension of the E8 loop group. The twist is in general necessary to cancel global anomalies due to the nontriviality of the 11dimensional 4form field strength G and due to the possible torsion present in the cycles the M5branes wrap. Our description of M5branes global anomalies leads to the D4branes one upon compactification of Mtheory to Type IIA theory. a