{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/50268"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/50268","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Exotic symplectic manifolds from Lefschetz fibrations","abstract":"In this thesis I construct, in all odd complex dimensions, pairs of Liouville domains W0 and W1 which are diffeomorphic to the cotangent bundle of the sphere with one extra subcritical handle, but are not symplectomorphic. While W0 is symplectically very similar to the cotangent bundle itself, W1 is more unusual. I use Seidel's exact triangles for Floer cohomology to show that the wrapped Fukaya category of W1 is trivial. As a corollary we obtain that W1 contains no compact exact Lagrangian submanifolds.","abstract_html":"In this thesis I construct, in all odd complex dimensions, pairs of Liouville domains W0 and W1 which are diffeomorphic to the cotangent bundle of the sphere with one extra subcritical handle, but are not symplectomorphic. While W0 is symplectically very similar to the cotangent bundle itself, W1 is more unusual. I use Seidel's exact triangles for Floer cohomology to show that the wrapped Fukaya category of W1 is trivial. As a corollary we obtain that W1 contains no compact exact Lagrangian submanifolds.","abstract_has_math":false,"creators":["Maydanskiy, Maksim (Maksim Igorevich)"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Mathematics.","school":null,"contributors":[],"advisors":["Denis Auroux."],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009","date_published":"2009","updated_at":"2026-07-22T22:21:44Z","subjects":["Mathematics."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/50268","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Denis Auroux."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Dept. of Mathematics."]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Massachusetts Institute of Technology. Dept. of Mathematics."]},{"key":"dc:creator","label":"Author","values":["Maydanskiy, Maksim (Maksim Igorevich)"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2010-01-07T15:49:33Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2010-01-07T15:49:33Z"]},{"key":"dc:date.issued","label":"Date","values":["2009"]},{"key":"dc:publisher","label":"Institution","values":["Massachusetts Institute of Technology"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/50268"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.","This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.","Includes bibliographical references (p. 43-44)."]},{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis I construct, in all odd complex dimensions, pairs of Liouville domains W0 and W1 which are diffeomorphic to the cotangent bundle of the sphere with one extra subcritical handle, but are not symplectomorphic. While W0 is symplectically very similar to the cotangent bundle itself, W1 is more unusual. I use Seidel's exact triangles for Floer cohomology to show that the wrapped Fukaya category of W1 is trivial. As a corollary we obtain that W1 contains no compact exact Lagrangian submanifolds."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Exotic symplectic manifolds from Lefschetz fibrations"]}]}],"canonical_facts":{"dc:contributor.advisor":["Denis Auroux."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:contributor.other":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:creator":["Maydanskiy, Maksim (Maksim Igorevich)"],"dc:date.accessioned":["2010-01-07T15:49:33Z"],"dc:date.available":["2010-01-07T15:49:33Z"],"dc:date.issued":["2009"],"dc:description":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.","This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.","Includes bibliographical references (p. 43-44)."],"dc:description.abstract":["In this thesis I construct, in all odd complex dimensions, pairs of Liouville domains W0 and W1 which are diffeomorphic to the cotangent bundle of the sphere with one extra subcritical handle, but are not symplectomorphic. While W0 is symplectically very similar to the cotangent bundle itself, W1 is more unusual. I use Seidel's exact triangles for Floer cohomology to show that the wrapped Fukaya category of W1 is trivial. As a corollary we obtain that W1 contains no compact exact Lagrangian submanifolds."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/50268"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Mathematics."],"dc:title":["Exotic symplectic manifolds from Lefschetz fibrations"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:21:44Z"}