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70
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
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
Localized homology
 In Shape Modeling International
, 2007
"... In this paper, we provide the theoretical foundation and an effective algorithm for localizing topological attributes such as tunnels and voids. Unlike previous work that focused on 2manifolds with restricted geometry, our theory is general and localizes arbitrarydimensional attributes in arbitrar ..."
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Cited by 19 (4 self)
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In this paper, we provide the theoretical foundation and an effective algorithm for localizing topological attributes such as tunnels and voids. Unlike previous work that focused on 2manifolds with restricted geometry, our theory is general and localizes arbitrarydimensional attributes in arbitrary spaces. We implement our algorithm to validate our approach in practice. 1
Orientations for pseudoholomorphic quilts
, 2007
"... We construct coherent orientations on moduli spaces of quilted pseudoholomorphic surfaces and determine the effect of various gluing operations on the orientations. We also investigate the behavior of the orientations under composition of Lagrangian correspondences. ..."
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Cited by 17 (10 self)
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We construct coherent orientations on moduli spaces of quilted pseudoholomorphic surfaces and determine the effect of various gluing operations on the orientations. We also investigate the behavior of the orientations under composition of Lagrangian correspondences.
Essentially Reductive Hilbert Modules
, 2004
"... Consider a Hilbert space obtained as the completion of the polynomials C[z] in mvariables for which the monomials are orthogonal. If the commuting weighted shifts defined by the coordinate functions are essentially normal, then the same is true for their restrictions to invariant subspaces spanned ..."
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Cited by 16 (7 self)
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Consider a Hilbert space obtained as the completion of the polynomials C[z] in mvariables for which the monomials are orthogonal. If the commuting weighted shifts defined by the coordinate functions are essentially normal, then the same is true for their restrictions to invariant subspaces spanned by monomials. This generalizes the result of Arveson [4] in which the Hilbert space is the mshift Hardy space H2 m. He establishes his result for the case of finite multiplicity and shows the selfcommutators lie in the Schatten pclass for p> m. We establish our result at the same level of generality. We also discuss the Khomology invariant defined in these cases. 0
Renormalization group flows and continual Lie algebras”, JHEP 0308
, 2003
"... We study the renormalization group flows of twodimensional metrics in sigma models using the oneloop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the worldsheet lengt ..."
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Cited by 15 (6 self)
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We study the renormalization group flows of twodimensional metrics in sigma models using the oneloop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the worldsheet length scale, t, is interpreted as Dynkin parameter on the root system of a novel continual Lie algebra, denoted by G(d/dt; 1), with antisymmetric Cartan kernel K(t, t ′ ) = δ ′ (t − t ′); as such, it coincides with the Cartan matrix of the superalgebra sl(NN + 1) in the large N limit. The resulting Toda field equation is a nonlinear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time, t. We provide the general solution of the renormalization group flows in terms of free fields, via Bäcklund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultraviolet limit by gluing together two copies of Witten’s twodimensional black hole in
The loop group of E8 and KTheory from 11d
 J. High Energy Phys
"... We examine the conjecture that an 11d E8 bundle, appearing in the calculation of phases in the MTheory partition function, plays a physical role in MTheory, focusing on consequences for the classification of string theory solitons. This leads for example to a classification of IIA solitons in term ..."
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Cited by 14 (5 self)
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We examine the conjecture that an 11d E8 bundle, appearing in the calculation of phases in the MTheory partition function, plays a physical role in MTheory, focusing on consequences for the classification of string theory solitons. This leads for example to a classification of IIA solitons in terms of that of LE8 bundles in 10d. Since K ( Z, 2) approximates LE8 up to π14, this reproduces the KTheoretic classification of IIA Dbranes while treating NSNS and RR solitons more symmetrically and providing a natural interpretation of G0 as the central extension of ˜ LE8.
Supersymmetric WZW models and twisted Ktheory of SO(3)
, 2004
"... We present an encompassing treatment of D–brane charges in supersymmetric SO(3) WZW models. There are two distinct supersymmetric CFTs at each even level: the standard bosonic SO(3) modular invariant tensored with free fermions, as well as a novel twisted model. We calculate the relevant twisted K–t ..."
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Cited by 14 (3 self)
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We present an encompassing treatment of D–brane charges in supersymmetric SO(3) WZW models. There are two distinct supersymmetric CFTs at each even level: the standard bosonic SO(3) modular invariant tensored with free fermions, as well as a novel twisted model. We calculate the relevant twisted K–theories and find complete agreement with the CFT analysis of D–brane charges. The K–theoretical computation in particular elucidates some important aspects of N = 1 supersymmetric WZW models on nonsimply connected Lie groups.