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Sep 18, 2013
09/13

by
A. L. Carey; Bai-Ling Wang

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We explain how multiplicative bundle gerbes over a compact, connected and simple Lie group $G$ lead to a certain fusion category of equivariant bundle gerbe modules given by pre-quantizable Hamiltonian $LG$-manifolds arising from Alekseev-Malkin-Meinrenken's quasi-Hamiltonian $G$-spaces. The motivation comes from string theory namely, by generalising the notion of $D$-branes in $G$ to allow subsets of $G$ that are the image of a $G$-valued moment map we can define a `fusion of $D$-branes' and a...

Source: http://arxiv.org/abs/math-ph/0505040v2

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Sep 21, 2013
09/13

by
Alan Carey; Matilde Marcolli; Bai-Ling Wang

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We establish a surgery formula for 3-dimensional Seiberg-Witten monopoles under (+1) Dehn surgery on a knot in a homology 3-sphere. (substantial revision)

Source: http://arxiv.org/abs/math/9907065v3

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Sep 19, 2013
09/13

by
Alan L. Carey; Bai-Ling Wang

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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 necessarily K-oriented). The push-forward map generalizes the push-forward map in ordinary K-theory for any $K$-oriented differentiable proper map and the Atiyah-Singer index theorem of Dirac operators on Clifford modules. For $D$-branes satisfying Freed-Witten's anomaly cancellation condition in a manifold with...

Source: http://arxiv.org/abs/math/0507414v4

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52

Sep 19, 2013
09/13

by
Alan L. Carey; Bai-Ling Wang

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This paper gives a detailed construction of Seiberg-Witten-Floer homology for a closed oriented 3-manifold with a non-torsion $\spinc$ structure. Gluing formulae for certain 4-dimensional manifolds splitting along an embedded 3-manifold are obtained.

Source: http://arxiv.org/abs/math/0206047v1

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Sep 21, 2013
09/13

by
Alan L. Carey; Bai-Ling Wang

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The goal of this paper is to apply the universal gerbe of \cite{CMi1} and \cite{CMi2} to give an alternative, simple and more unified view of the relationship between index theory and gerbes. We discuss determinant bundle gerbes \cite{CMMi1} and the index gerbe of \cite{L} for the case of families of Dirac operators on odd dimensional closed manifolds. The method also works for a family of Dirac operators on odd dimensional manifolds with boundary, for a pair of Melrose-Piazza's...

Source: http://arxiv.org/abs/math/0407243v2

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Sep 19, 2013
09/13

by
Alan L. Carey; Bai-Ling Wang

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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 charges in Type I and Type II string theory are classified by twisted KO-theory and twisted K-theory respectively in the presence of B-fields as proposed by Witten.

Source: http://arxiv.org/abs/0909.4848v1

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Sep 19, 2013
09/13

by
Alan L. Carey; Jouko Mickelsson; Bai-Ling Wang

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In this paper, we develop differential twisted K-theory and define a twisted Chern character on twisted K-theory which depends on a choice of connection and curving on the twisting gerbe. We also establish the general Riemann-Roch theorem in twisted K-theory and find some applications in the study of twisted K-theory of compact simple Lie groups.

Source: http://arxiv.org/abs/0708.3114v4

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Sep 20, 2013
09/13

by
Alan L. Carey; Stuart Johnson; Michael K. Murray; Danny Stevenson; Bai-Ling Wang

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We develop the theory of Chern-Simons bundle 2-gerbes and multiplicative bundle gerbes associated to any principal $G$-bundle with connection and a class in $H^4(BG, \ZZ)$ for a compact semi-simple Lie group $G$. The Chern-Simons bundle 2-gerbe realises differential geometrically the Cheeger-Simons invariant. We apply these notions to refine the Dijkgraaf-Witten correspondence between three dimensional Chern-Simons functionals and Wess-Zumino-Witten models associated to the group $G$. We do...

Source: http://arxiv.org/abs/math/0410013v2

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Jun 26, 2018
06/18

by
Bohui Chen; An-Min Li; Bai-Ling Wang

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In this paper, we explore the theme of orbifold stratified spaces and establish a general criterion for them to be smooth orbifolds. This criterion utilizes the notion of linear stratification on the gluing bundles for the orbifold stratified spaces. We introduce a concept of good gluing structure to ensure a smooth structure on the stratified space. As an application, we provide an orbifold structure on the coarse moduli space $\bar{M}_{g, n}$ of stable genus $g$ curves with $n$-marked points....

Topics: Mathematics, Geometric Topology, Symplectic Geometry

Source: http://arxiv.org/abs/1502.05103