dc.contributor.advisor Ünlü, Özgün en_US dc.contributor.author Şentürk, Berrin en_US dc.date.accessioned 2018-09-18T07:50:58Z dc.date.available 2018-09-18T07:50:58Z dc.date.copyright 2018-09 dc.date.issued 2018-09 dc.date.submitted 2018-09-17 dc.identifier.uri http://hdl.handle.net/11693/47886 dc.description Cataloged from PDF version of article. en_US dc.description Thesis (Ph.D.): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2018. en_US dc.description Includes bibliographical references (leaves 66-68). en_US dc.description.abstract A well-known conjecture states that if an elementary abelian p-group acts en_US 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. dc.description.statementofresponsibility by Berrin Şentürk. en_US dc.format.extent vii, 68 leaves : charts ; 30 cm. en_US dc.language.iso English en_US dc.rights info:eu-repo/semantics/openAccess en_US dc.subject Rank Conjecture en_US dc.subject Projective Variety en_US dc.subject Borel Orbit en_US dc.title A conjecture on square-zero upper triangular matrices and Carlsson's rank conjecture en_US dc.title.alternative Karesi sıfır üst üçgensel matrisler üzerinde bir sanı ve Carlsson'ın mertebe sanısı en_US dc.type Thesis en_US dc.department Department of Mathematics en_US dc.publisher Bilkent University en_US dc.description.degree Ph.D. en_US dc.identifier.itemid B159012
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