dc.contributor.advisor | Ünlü, Özgün | |
dc.contributor.author | Şentürk, Berrin | |
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
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.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 | |