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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

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5.0

Jun 30, 2018
06/18

by
Bohui Chen; Bai-Ling Wang

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Let $(X,\omega)$ be a compact symplectic manifold with a Hamiltonian action of a compact Lie group $G$ and $\mu: X\to \mathfrak g$ be its moment map. In this paper, we study the $L^2$-moduli spaces of symplectic vortices on Riemann surfaces with cylindrical ends. We studied a circle-valued action functional whose gradient flow equation corresponds to the symplectic vortex equations on a cylinder $S^1\times \mathbb R$. Assume that $0$ is a regular value of the moment map $\mu$, we show that the...

Topics: Symplectic Geometry, Mathematics

Source: http://arxiv.org/abs/1405.6387

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10.0

Jun 30, 2018
06/18

by
Paulo Carrillo Rouse; Bai-Ling Wang

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We construct the geometric Baum-Connes assembly map for twisted Lie groupoids, that means for Lie groupoids together with a given groupoid equivariant $PU(H)-$principle bundle. The construction is based on the use of geometric deformation groupoids, these objects allow in particular to give a geometric construction of the associated pushforward maps and to establish the functoriality. The main results in this paper are to define the geometric twisted K-homology groups and to construct the...

Topics: Mathematics, K-Theory and Homology, Operator Algebras, Geometric Topology

Source: http://arxiv.org/abs/1402.3456