{"id":440,"date":"2024-02-26T19:24:55","date_gmt":"2024-02-26T17:24:55","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/gentle\/?p=440"},"modified":"2026-05-14T08:49:58","modified_gmt":"2026-05-14T06:49:58","slug":"new-geometric-structures-on-3-manifolds-surgery-and-generalized-geometry-2","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/gentle\/2024\/02\/26\/new-geometric-structures-on-3-manifolds-surgery-and-generalized-geometry-2\/","title":{"rendered":"New geometric structures on 3-manifolds: surgery and generalized geometry"},"content":{"rendered":"<p>Paper by J. Porti and R. Rubio.<\/p>\n<p>To appear in Advances in Mathematics.<\/p>\n<p>Abstract: Cosymplectic and normal almost contact structures are analogues of symplectic and complex structures that can be defined on 3-manifolds. Their existence imposes strong topological constraints. Generalized geometry offers a natural common generalization of these two structures: <span id=\"MathJax-Element-1-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"msubsup\"><span id=\"MathJax-Span-4\" class=\"mi\">B<\/span><sub><span id=\"MathJax-Span-5\" class=\"mn\">3<\/span><\/sub><\/span><\/span><\/span><\/span>-generalized complex structures. We prove that any closed orientable 3-manifold admits such a structure, which can be chosen to be stable, that is, generically cosymplectic up to generalized diffeomorphism.<\/p>\n<p>Find it on the <a href=\"https:\/\/arxiv.org\/abs\/2402.12471\">arXiv (2402.12471).<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Paper by J. Porti and R. Rubio. To appear in Advances in Mathematics. Abstract: Cosymplectic and normal almost contact structures are analogues of symplectic and complex structures that can be defined on 3-manifolds. Their existence imposes strong topological constraints. Generalized geometry offers a natural common generalization of these two structures: B3-generalized complex structures. We prove [&hellip;]<\/p>\n","protected":false},"author":54,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[51,34],"tags":[],"class_list":["post-440","post","type-post","status-publish","format-standard","hentry","category-papers","category-rubio"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts\/440","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/users\/54"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/comments?post=440"}],"version-history":[{"count":2,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts\/440\/revisions"}],"predecessor-version":[{"id":761,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts\/440\/revisions\/761"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/media?parent=440"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/categories?post=440"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/tags?post=440"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}