{"id":1274,"date":"2024-01-14T19:45:43","date_gmt":"2024-01-14T18:45:43","guid":{"rendered":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/?p=1274"},"modified":"2024-02-17T21:15:16","modified_gmt":"2024-02-17T20:15:16","slug":"phd-course-foliations","status":"publish","type":"post","link":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/2024\/01\/14\/phd-course-foliations\/","title":{"rendered":"PhD Course: Foliations"},"content":{"rendered":"

Foliations<\/span><\/h1>\n

Prof. Gianluca Bande<\/b>
\nDipartimento di Matematica e Informatica
\nUniversit\u00e0 degli Studi di Cagliari<\/span><\/p>\n

Abstract<\/b><\/span><\/p>\n

The course is an introduction to the Theory of Foliations. Basic knowledge of Differential Geometry is required and the basics of Fundamental Group.<\/span><\/span><\/p>\n

Outline<\/b><\/span><\/p>\n

– Definition(s) and examples of Foliations. Dynamical systems. Frobenius\u2019 Theorem.
\n<\/span>– Holonomy of a leaf and the Reeb Stability Theorem. Basic and foliated Cohomology. Godbillion-Vey class for a codimension 1 foliation on a 3-manifold.
\n– The Reeb foliation: definition and a 3D-printer model. Novikov and Likorisch Theorem.<\/span><\/span><\/p>\n

Schedule<\/b><\/span><\/p>\n

The course spans over 3 lectures of 2 hours each (6 hours total). The lectures will be given on February 5, February 12, February 15 \u2013 2024 at 4:30 p.m. in Room B of the Department of Mathematics and Computer Science.<\/span><\/span><\/p>\n

Exam<\/b><\/span><\/p>\n

The final exam consists in a presentation.<\/span><\/span><\/p>\n

References<\/b><\/span><\/p>\n

1. C. <\/span>Camacho and A. Lins Neto, <\/span>Geometric theory of foliations<\/span><\/strong>, Birkh\u00e4user, 1985.
\n2. <\/span>A. Candel;\u00a0L. <\/span>Conlon, <\/span>Foliations I<\/span><\/strong>, Grad. Stud. Math.\u00a023, American Mathematical Society,\u00a0Providence, 2000.
\n3. <\/span>P. Tondeur, <\/span>Geometry of Foliations<\/span><\/strong>, Monogr. Math 90, <\/span>Birkh\u00e4user Verlag,\u00a0Basel<\/span>,<\/em>\u00a01997.<\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Foliations Prof. Gianluca Bande Dipartimento di Matematica e Informatica Universit\u00e0 degli Studi di Cagliari Abstract The course is an introduction to the Theory of Foliations. Basic knowledge of Differential Geometry is required and the basics of Fundamental Group. Outline – Definition(s) and examples of Foliations. Dynamical systems. Frobenius\u2019 Theorem. – Holonomy of a leaf and the Reeb Stability Theorem. Basic and foliated Cohomology. Godbillion-Vey class for a codimension 1 foliation on a 3-manifold. – The Reeb foliation: definition and a 3D-printer model. Novikov and Likorisch Theorem. Schedule The course spans over 3 lectures of 2 hours each (6 hours total). […]<\/a><\/p>\n","protected":false},"author":244,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,10],"tags":[],"class_list":["post-1274","post","type-post","status-publish","format-standard","hentry","category-dipartimento-matematica-informatica","category-events","category-9-id","category-10-id","post-seq-1","post-parity-odd","meta-position-corners","fix"],"_links":{"self":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts\/1274","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/users\/244"}],"replies":[{"embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/comments?post=1274"}],"version-history":[{"count":5,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts\/1274\/revisions"}],"predecessor-version":[{"id":1299,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts\/1274\/revisions\/1299"}],"wp:attachment":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/media?parent=1274"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/categories?post=1274"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/tags?post=1274"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}