Şentürk, Berrin2016-01-082016-01-082011http://hdl.handle.net/11693/15228Ankara : The Department of Mathematics and the Institute of Engineering and Science of Bilkent University, 2011.Thesis (Master's) -- Bilkent University, 2011.Includes bibliographical references leaves 36-37.Gunnar Carlsson stated a conjecture which gives a lower bound on the rank of a differential graded module over a polynomial ring with coefficients in algebraically closed field k when it has a finite dimensional homology over k. Carlsson showed that this conjecture implies the rank conjecture about free actions on product of spheres. In this paper, to understand the Carlsson’s conjecture about differential graded modules, we study the structure of the variety of upper triangular square zero matrices and the techniques which were investigated by Rothbach to determine its irreducible components . We hope these varieties could help prove Carlsson’s conjecture.vi, 37 leavesEnglishinfo:eu-repo/semantics/openAccessdifferential graded modulefree actionvarietyQA188 .S45 2011Matrices.Polynomial rings.Rings (Algebra)Finite groups.Algebra, Homological.Thesis