Smooth s-cobordisms of elliptic 3-manifolds
TLDR
The main result of as mentioned in this paper is that a smooth s-cobordism of elliptic 3-manifolds is diffeomorphic to a product (assuming a canonical contact structure on the boundary).Abstract:
The main result of this paper states that a symplectic s-cobordism of elliptic 3-manifolds is diffeomorphic to a product (assuming a canonical contact structure on the boundary). Based on this theorem, we conjecture that a smooth s-cobordism of elliptic 3-manifolds is smoothly a product if its universal cover is smoothly a product. We explain how the conjecture fits naturally into the program of Taubes of constructing symplectic structures on an oriented smooth 4-manifold with b + ≥ 1 from generic self-dual harmonic forms. The paper also contains an auxiliary result of independent interest, which generalizes Taubes’ theorem “SW ⇒ Gr” to the case of symplectic 4-orbifolds.read more
Citations
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Numerical simulation of seawater intrusion to coastal aquifers and brine water/freshwater interaction in south coast of Laizhou Bay, China
Yawen Chang,Bill X. Hu,Bill X. Hu,Zexuan Xu,Xue Li,Juxiu Tong,Lin Chen,Hanxiong Zhang,Jinjie Miao,Hongwei Liu,Zhen Ma +10 more
TL;DR: In this article, a two-dimensional SEAWAT model is developed to simulate the seawater intrusion to coastal aquifers and brine water/fresh water interaction in the south of Laizhou Bay.
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Pseudoholomorphic curves in four-orbifolds and some applications
TL;DR: The pseudoholomorphic curve theory of Gromov, McDuff and Taubes on 4-manifolds and Seiberg-Witten theory on elliptic 3-mansifolds is discussed in this article.
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On a notion of maps between orbifolds, I. function spaces
TL;DR: In this article, it was shown that the space of such maps of C^r-class between smooth orbifolds has a natural Banach orbifold structure if the domain of the map is compact, generalizing the corresponding result in the manifold case.
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On a notion of maps between orbifolds ii: homotopy and cw-complex
TL;DR: In this paper, the second part of a series of papers devoted to a comprehensive theory of maps between orbifolds is devoted to the construction of a set of algebraic invariants and an analog of CW-complex theory.
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On a notion of maps between orbifolds I. Function spaces
TL;DR: In this article, it was shown that the space of such maps of Cr class between smooth orbifolds has a natural Banach orbifold structure if the domain of the map is compact, generalizing the corresponding result in the manifold case.
References
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Pseudo holomorphic curves in symplectic manifolds
TL;DR: In this article, the authors define a parametrized (pseudo holomorphic) J-curve in an almost complex manifold (IS, J) is a holomorphic map of a Riemann surface into Is, say f : (S, J3 ~(V, J).
Journal ArticleDOI
The geometries of 3-manifolds
TL;DR: The theory of 3-manifolds has been revolutionised in the last few years by work of Thurston as mentioned in this paper, who has shown that geometry has an important role to play in the theory in addition to the use of purely topological methods.
Book
J-Holomorphic Curves and Symplectic Topology
Dusa McDuff,Dietmar Salamon +1 more
TL;DR: The theory of $J$-holomorphic curves has been of great importance since its introduction by Gromov in 1985 as mentioned in this paper, and its applications include many key results in symplectic topology.