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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 16 (4 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 15 (3 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
Generating Functional In CFT And Effective Action For TwoDimensional Quantum Gravity On Higher Genus Riemann Surfaces
 Comm. Math. Phys
, 1996
"... . We formulate and solve the analog of the universal Conformal Ward Identity for the stressenergy tensor on a compact Riemann surface of genus g ? 1, and present a rigorous invariant formulation of the chiral sector in the induced twodimensional gravity on higher genus Riemann surfaces. Our constr ..."
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Cited by 12 (7 self)
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. We formulate and solve the analog of the universal Conformal Ward Identity for the stressenergy tensor on a compact Riemann surface of genus g ? 1, and present a rigorous invariant formulation of the chiral sector in the induced twodimensional gravity on higher genus Riemann surfaces. Our construction of the action functional uses various double complexes naturally associated with a Riemann surface, with computations that are quite similar to descent calculations in BRST cohomology theory. We also provide an interpretation of the action functional in terms of the geometry of different fiber spaces over the Teichmuller space of compact Riemann surfaces of genus g ? 1. 1. Introduction Conformal symmetry in two dimensions, according to Belavin, Polyakov, and Zamolodchikov [8], is generated by the holomorphic and antiholomorphic components T(z) and ¯ T(¯z) of the stressenergy tensor of a Conformal Field Theory. These components satisfy the Operator Product Expansions [8, 15] T(z)...
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 11 (5 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
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 11 (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.
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 8 (7 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.
The stable rank of topological algebras and a problem of R
 G. Swan, J. Functional Analysis
, 1998
"... Abstract. Various notions of stable ranks are studied for topological algebras. Some partial answers to R.G. Swan’s problem (Have two Banach or good Fréchet algebras as in the density theorem in Ktheory the same stable rank?) are obtained. For example, a Fréchet dense ∗subalgebra A of a C ∗algebr ..."
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Cited by 8 (0 self)
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Abstract. Various notions of stable ranks are studied for topological algebras. Some partial answers to R.G. Swan’s problem (Have two Banach or good Fréchet algebras as in the density theorem in Ktheory the same stable rank?) are obtained. For example, a Fréchet dense ∗subalgebra A of a C ∗algebra B, closed under C ∞functional calculus of selfadjoint elements, has the same Bass stable rank as B.
The Ktheory of abelian symplectic quotients
, 2008
"... ABSTRACT. Let T be a compact torus and (M, ω) a Hamiltonian Tspace. In a previous paper, the authors showed that the Tequivariant Ktheory of the manifold M surjects onto the ordinary integral Ktheory of the symplectic quotient M//T, under certain technical conditions on the moment map. In this p ..."
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Cited by 6 (2 self)
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ABSTRACT. Let T be a compact torus and (M, ω) a Hamiltonian Tspace. In a previous paper, the authors showed that the Tequivariant Ktheory of the manifold M surjects onto the ordinary integral Ktheory of the symplectic quotient M//T, under certain technical conditions on the moment map. In this paper, we use equivariant Morse theory to give a method for computing the Ktheory of M//T by obtaining an explicit description of the kernel of the surjection κ: K ∗ T(M) ։ K ∗ (M//T). Our results are Ktheoretic analogues of the work of Tolman and Weitsman for Borel equivariant cohomology. Further, we prove that under suitable technical conditions on the Torbit stratification of M, there is an explicit GoreskyKottwitzMacPherson (“GKM”) type combinatorial description of the Ktheory of a Hamiltonian Tspace in terms of fixed point data. Finally, we illustrate our methods by computing the ordinary Ktheory of compact symplectic toric manifolds, which arise as symplectic quotients of an affine space C N by a linear torus action. CONTENTS