A conjecture on square-zero upper triangular matrices and Carlsson's rank conjecture

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buir.advisorÜnlü, Özgün
dc.contributor.authorŞentürk, Berrin
dc.date.accessioned2018-09-18T07:50:58Z
dc.date.available2018-09-18T07:50:58Z
dc.date.copyright2018-09
dc.date.issued2018-09
dc.date.submitted2018-09-17
dc.descriptionCataloged from PDF version of article.en_US
dc.descriptionThesis (Ph.D.): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2018.en_US
dc.descriptionIncludes bibliographical references (leaves 66-68).en_US
dc.description.abstractA well-known conjecture states that if an elementary abelian p-group acts freely on a product of spheres, then the rank of the group is at most the number of spheres in the product. Carlsson gives an algebraic version of this conjecture by considering a di erential graded module M over the polynomial ring A in r variables: If the homology of M is nontrivial and nite dimensional over the ground eld, then N := dimAM is at least 2r. In this thesis, we state a stronger conjecture concerning varieties of square-zero upper triangular N N matrices with entries in A. By stratifying these varieties via Borel orbits, we show that the stronger conjecture holds when N < 8 or r < 3. As a consequence, we obtain a new proof for many of the known cases of Carlsson's conjecture as well as novel results for N > 4 and r = 2.en_US
dc.description.provenanceSubmitted by Betül Özen (ozen@bilkent.edu.tr) on 2018-09-18T07:50:58Z No. of bitstreams: 1 BerrinSenturkDoktoraTEZ.pdf: 456356 bytes, checksum: f16271a5689123b20a0713ad611e06f3 (MD5)en
dc.description.provenanceMade available in DSpace on 2018-09-18T07:50:58Z (GMT). No. of bitstreams: 1 BerrinSenturkDoktoraTEZ.pdf: 456356 bytes, checksum: f16271a5689123b20a0713ad611e06f3 (MD5) Previous issue date: 2018-09en
dc.description.statementofresponsibilityby Berrin Şentürk.en_US
dc.format.extentvii, 68 leaves : charts ; 30 cm.en_US
dc.identifier.itemidB159012
dc.identifier.urihttp://hdl.handle.net/11693/47886
dc.language.isoEnglishen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectRank Conjectureen_US
dc.subjectProjective Varietyen_US
dc.subjectBorel Orbiten_US
dc.titleA conjecture on square-zero upper triangular matrices and Carlsson's rank conjectureen_US
dc.title.alternativeKaresi sıfır üst üçgensel matrisler üzerinde bir sanı ve Carlsson'ın mertebe sanısıen_US
dc.typeThesisen_US
thesis.degree.disciplineMathematics
thesis.degree.grantorBilkent University
thesis.degree.levelDoctoral
thesis.degree.namePh.D. (Doctor of Philosophy)

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