Smooth s-cobordisms of elliptic 3-manifolds

Weimin Chen

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arXiv · math/0403396

Smooth s-cobordisms of elliptic 3-manifolds

Weimin Chen

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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 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.

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Weimin Chen. 2006-03-28. Smooth s-cobordisms of elliptic 3-manifolds. https://arxiv.org/abs/math/0403396

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