Symplectic torus bundles and group extensions
Symplectic torus bundles $\xi:T^{2}\to E\to B$ are classified by the second cohomology group of $B$ with local coefficients $H_{1}(T^{2})$. For $B$ a compact, orientable surface, the main theorem of this paper gives a necessary and sufficient condition on the cohomology class corresponding to $\xi$...
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| creator | Kahn, Peter J |
| description | Symplectic torus bundles $\xi:T^{2}\to E\to B$ are classified by the second
cohomology group of $B$ with local coefficients $H_{1}(T^{2})$. For $B$ a
compact, orientable surface, the main theorem of this paper gives a necessary
and sufficient condition on the cohomology class corresponding to $\xi$ for $E$
to admit a symplectic structure compatible with the symplectic bundle structure
of $\xi$ : namely, that it be a torsion class. The proof is based on a
group-extension-theoretic construction of J. Huebschmann (Sur les premieres
differentielles de la suite spectrale cohomologique d'une extension de groupes,
C.R. Acad. Sc. Paris, Serie A, tome 285, 28 novembre 1977, 929-931). A key
ingredient is the notion of fibrewise-localization. |
| doi_str_mv | 10.48550/arxiv.math/0405109 |
| format | Article |
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cohomology group of $B$ with local coefficients $H_{1}(T^{2})$. For $B$ a
compact, orientable surface, the main theorem of this paper gives a necessary
and sufficient condition on the cohomology class corresponding to $\xi$ for $E$
to admit a symplectic structure compatible with the symplectic bundle structure
of $\xi$ : namely, that it be a torsion class. The proof is based on a
group-extension-theoretic construction of J. Huebschmann (Sur les premieres
differentielles de la suite spectrale cohomologique d'une extension de groupes,
C.R. Acad. Sc. Paris, Serie A, tome 285, 28 novembre 1977, 929-931). A key
ingredient is the notion of fibrewise-localization.</description><identifier>DOI: 10.48550/arxiv.math/0405109</identifier><language>eng</language><subject>Mathematics - Algebraic Topology ; Mathematics - Symplectic Geometry</subject><creationdate>2004-05</creationdate><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/math/0405109$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.math/0405109$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Kahn, Peter J</creatorcontrib><title>Symplectic torus bundles and group extensions</title><description>Symplectic torus bundles $\xi:T^{2}\to E\to B$ are classified by the second
cohomology group of $B$ with local coefficients $H_{1}(T^{2})$. For $B$ a
compact, orientable surface, the main theorem of this paper gives a necessary
and sufficient condition on the cohomology class corresponding to $\xi$ for $E$
to admit a symplectic structure compatible with the symplectic bundle structure
of $\xi$ : namely, that it be a torsion class. The proof is based on a
group-extension-theoretic construction of J. Huebschmann (Sur les premieres
differentielles de la suite spectrale cohomologique d'une extension de groupes,
C.R. Acad. Sc. Paris, Serie A, tome 285, 28 novembre 1977, 929-931). A key
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cohomology group of $B$ with local coefficients $H_{1}(T^{2})$. For $B$ a
compact, orientable surface, the main theorem of this paper gives a necessary
and sufficient condition on the cohomology class corresponding to $\xi$ for $E$
to admit a symplectic structure compatible with the symplectic bundle structure
of $\xi$ : namely, that it be a torsion class. The proof is based on a
group-extension-theoretic construction of J. Huebschmann (Sur les premieres
differentielles de la suite spectrale cohomologique d'une extension de groupes,
C.R. Acad. Sc. Paris, Serie A, tome 285, 28 novembre 1977, 929-931). A key
ingredient is the notion of fibrewise-localization.</abstract><doi>10.48550/arxiv.math/0405109</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Algebraic Topology Mathematics - Symplectic Geometry |
| title | Symplectic torus bundles and group extensions |
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