Minimal models of some differential graded modules

Let $k$ be an algebraically closed field of characteristic $2$. Carlsson showed the existence of minimal models of certain semifree differential graded $k[x_1,\ldots,x_r]$-modules. Here we give an explicit construction of these minimal models without the semifreeness condition. We also prove Carlsson's rank conjecture when the degrees of all nonzero homology groups of a differential graded module have the same parity. Dually, we construct minimal models of chain complexes of Borel constructions of spaces with a free $(\mathbb{Z}/2)^r$-action. These minimal models are called minimal Hirsch-Brown models by Allday-Puppe. Puppe also showed that putting certain multiplicative structures on these minimal models could be useful to improve known results on related conjectures. Here we give our construction of these models using operadic language. This enables us to put multiplicative structures on these models.Comment: 8 page

Free actions on CW-complexes and varieties of square zero matrices

Ankara : 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.Şentürk, BerrinM.S

Karesi sıfır üst üçgensel matrisler üzerinde bir sanı ve Carlsson'ın mertebe sanısı

Cataloged from PDF version of article.Thesis (Ph.D.): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2018.Includes bibliographical references (leaves 66-68).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.by Berrin Şentürk.Ph.D

Effects of grape pomace supplementation to laying hen diet on performance, egg quality, egg lipid peroxidation and some biochemical parameters

This study was carried out to determine the effects of dried grape pomace supplementation in a corn-soy-based diet on performance, egg quality, plasma and egg lipid peroxidation, and some biochemical parameters of laying hens. In this study, 96 moulted 80-week-old Bovans laying hens were distributed into three groups with eight replicates. The hens were fed a supplemented diet with 0% (control group), 4% and 6% grape pomace (experimental groups) for 12 weeks. In the study, the effects of grape pomace supplementation in a corn-soy-based diet on performance, internal and external egg quality, serum total cholesterol, total protein, glucose and triglyceride levels, and plasma and egg yolk malondialdehyde (MDA) levels were determined. The addition of grape pomace to laying hen diet did not significantly affect live weight, feed intake, egg production and feed efficiency (P > 0.05). In all treatment groups, supplementation did not significantly affect albumen index, Haugh unit, egg yolk index, yolk colour, eggshell ratio, eggshell thickness, egg-specific gravity, total cholesterol, total protein and triglyceride compared to the control group (P > 0.05). In the study, 4% grape pomace supplementation to diet significantly increased egg weight (P < 0.001), and both 4% and 6% grape pomace supplementation levels significantly increased liver weight (P < 0.05) and liver weight ratio (P < 0.01). Grape pomace addition to laying hens diet significantly decreased plasma MDA and serum glucose levels (P < 0.001). Also, grape pomace addition significantly decreased egg yolk MDA levels on day 1 (incubation on 0 minute; P < 0.001), and day 15 [incubation on 0, 30, 60 and 90 (P < 0.05) minutes]. The results of this study concluded that performance, egg quality and serum total cholesterol, total protein and triglyceride levels were not negatively affected. Plasma and egg yolk MDA, and serum glucose levels were reduced by 4% and 6% supplementation to laying hen diets. It was concluded that grape pomace supplementation has the potential to extend shelf life