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Creators/Authors contains: "Wang, Donghao"

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  1. (, ArXivorg)
    This is the second paper of this series. We define the monopole Floer homol- ogy for 3-manifolds with torus boundary, extending the work of Kronheimer-Mrowka for closed 3-manifolds. The Euler characteristic of this Floer homology recovers the Milnor torsion invariant of the 3-manifold by a theorem of Meng-Taubes. 
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    Accepted Manuscript Full Text Available
  2. (, ArXivorg)
    The end point of this series of papers is to construct the monopole Floer ho- mology for 3-manifolds with torus boundary. In the first paper, we explain the idea from the standpoint of gauged Landau-Ginzburg models and address a few model problems related to the compactness of moduli spaces, using a Bochner-type formula associated to the gauged Witten equations. 
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    Accepted Manuscript Full Text Available
  3. (, ArXiv.org)
    Let $$X=\mathbb{C}\times\Sigma$$ be the product of the complex plane and a compact Riemann surface. We establish a classification theorem of solutions to the Seiberg-Witten equation on $$X$$ with finite analytic energy. The spin bundle $$S^+\to X$$ splits as $$L^+\oplus L^-$$. When $$2-2g\leq c_1(S^+)[\Sigma]<0$$, the moduli space is in bijection with the moduli space of pairs $$((L^+,\bar{\partial}), f)$$ where $$(L^+,\bar{\partial})$$ is a holomorphic structure on $L^+$ and $$f: \mathbb{C}\to H^0(\Sigma, L^+,\bar{\partial})$$ is a polynomial map. Moreover, the solution has analytic energy $$-4\pi^2d\cdot c_1(S^+)[\Sigma]$$ if $$f$$ has degree $$d$$. When $$c_1(S^+)=0$$, all solutions are reducible and the moduli space is the space of flat connections on $$\bigwedge^2 S^+$$. We also estimate the decay rate at infinity for these solutions. 
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    Accepted Manuscript Full Text Available