Symplectic resolutions, Lefschetz property and formality
<p>We introduce a method to resolve a <em>symplectic orbifold</em>(<em>M</em>,<em>ω</em>) into a smooth symplectic manifold <sup>−</sup><sub style="position: relative; left: -.7em;">M</sub>, <sup>−</sup><sub s...
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| Format: | Journal article |
| Language: | English |
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Elsevier
2008
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| _version_ | 1797081709168033792 |
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| author | Cavalcanti, G Fernández, M Muñoz, V |
| author_facet | Cavalcanti, G Fernández, M Muñoz, V |
| author_sort | Cavalcanti, G |
| collection | OXFORD |
| description | <p>We introduce a method to resolve a <em>symplectic orbifold</em>(<em>M</em>,<em>ω</em>) into a smooth symplectic manifold <sup>−</sup><sub style="position: relative; left: -.7em;">M</sub>, <sup>−</sup><sub style="position: relative; left: -.6em;">ω</sub>. Then we study how the formality and the Lefschetz property of <sup>−</sup><sub style="position: relative; left: -.7em;">M</sub>, <sup>−</sup><sub style="position: relative; left: -.6em;">ω</sub> are compared with that of (<em>M</em>,<em>ω</em>). We also study the formality of the symplectic blow-up of (<em>M</em>,<em>ω</em>) along symplectic submanifolds disjoint from the orbifold singularities. This allows us to construct the first example of a simply connected compact symplectic manifold of dimension 8 which satisfies the Lefschetz property but is not formal, therefore giving a counter-example to a conjecture of Babenko and Taimanov.</p> |
| first_indexed | 2024-03-07T01:17:47Z |
| format | Journal article |
| id | oxford-uuid:8f4c8626-1c59-48cc-a0ea-506485906ef2 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:17:47Z |
| publishDate | 2008 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:8f4c8626-1c59-48cc-a0ea-506485906ef22022-03-26T23:03:20ZSymplectic resolutions, Lefschetz property and formalityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:8f4c8626-1c59-48cc-a0ea-506485906ef2MathematicsEnglishOxford University Research Archive - ValetElsevier2008Cavalcanti, GFernández, MMuñoz, V<p>We introduce a method to resolve a <em>symplectic orbifold</em>(<em>M</em>,<em>ω</em>) into a smooth symplectic manifold <sup>−</sup><sub style="position: relative; left: -.7em;">M</sub>, <sup>−</sup><sub style="position: relative; left: -.6em;">ω</sub>. Then we study how the formality and the Lefschetz property of <sup>−</sup><sub style="position: relative; left: -.7em;">M</sub>, <sup>−</sup><sub style="position: relative; left: -.6em;">ω</sub> are compared with that of (<em>M</em>,<em>ω</em>). We also study the formality of the symplectic blow-up of (<em>M</em>,<em>ω</em>) along symplectic submanifolds disjoint from the orbifold singularities. This allows us to construct the first example of a simply connected compact symplectic manifold of dimension 8 which satisfies the Lefschetz property but is not formal, therefore giving a counter-example to a conjecture of Babenko and Taimanov.</p> |
| spellingShingle | Mathematics Cavalcanti, G Fernández, M Muñoz, V Symplectic resolutions, Lefschetz property and formality |
| title | Symplectic resolutions, Lefschetz property and formality |
| title_full | Symplectic resolutions, Lefschetz property and formality |
| title_fullStr | Symplectic resolutions, Lefschetz property and formality |
| title_full_unstemmed | Symplectic resolutions, Lefschetz property and formality |
| title_short | Symplectic resolutions, Lefschetz property and formality |
| title_sort | symplectic resolutions lefschetz property and formality |
| topic | Mathematics |
| work_keys_str_mv | AT cavalcantig symplecticresolutionslefschetzpropertyandformality AT fernandezm symplecticresolutionslefschetzpropertyandformality AT munozv symplecticresolutionslefschetzpropertyandformality |