4-Manifolds With Inequivalent Symplectic Forms and 3-Manifolds With Inequivalent Fibrations

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4-Manifolds With Inequivalent Symplectic Forms and 3-Manifolds With Inequivalent Fibrations

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Title: 4-Manifolds With Inequivalent Symplectic Forms and 3-Manifolds With Inequivalent Fibrations
Author: McMullen, Curtis T.; Taubes, Clifford H.

Note: Order does not necessarily reflect citation order of authors.

Citation: McMullen, Curtis T., and Cliffor H. Taubes. 1999. 4-Manifolds with inequivalent symplectic forms and 3-manifolds with inequivalent fibrations. Mathematical Research Letters 6(5-6): 681–696. Revised 2003.
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Abstract: We exhibit a closed, simply connected 4-manifold \(X\) carrying two symplectic structures whose first Chern classes in \(H^2 (X, \mathbb{Z})\) lie in disjoint orbits of the diffeomorphism group of \(X\). Consequently, the moduli space of symplectic forms on \(X\) is disconnected. The example \(X\) is in turn based on a 3-manifold \(M\). The symplectic structures on \(X\) come from a pair of fibrations \(\pi_0, \pi_1 : M \rightarrow S^1\) whose Euler classes lie in disjoint orbits for the action of \( \mathrm{Diff}(M) \) on \(H_1(M, \mathbb{R})\).
Published Version: http://www.mrlonline.org/mrl/
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:3637160

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  • FAS Scholarly Articles [7078]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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