Algebraic topology
1. Invariant elements in the dual Steenrod algebra

T. Vergili; I. Karaca

Volume 08, Issue 03 , Summer 2019, , Pages 167-172

Abstract
  ‎In this paper‎, ‎we investigate the invariant elements of the dual mod $p$ Steenrod subalgebra ${\mathcal{A}_p}^*$ under the conjugation map $\chi$ and give bounds on the dimensions of $(\chi-1)({\mathcal{A}_p}^*)_d$‎, ‎where $({\mathcal{A}_p}^*)_d$ is the dimension of ${\mathcal{A}_p}^*$ ...  Read More

Algebraic topology
2. Digital cohomology groups of certain minimal surfaces

I. Karaca; O. Ege

Volume 07, Issue 04 , Autumn 2018, , Pages 293-305

Abstract
  In this study, we compute simplicial cohomology groups with different coefficients of a connected sum of certain minimal simple surfaces by using the universal coefficient theorem for cohomology groups. The method used in this paper is a different way to compute digital cohomology groups ...  Read More

Algebraic topology
3. A note on the new basis in the mod 2 Steenrod algebra

T. Vergili; I. Karaca

Volume 07, Issue 02 , Spring 2018, , Pages 101-107

Abstract
  ‎The Mod $2$ Steenrod algebra is a Hopf algebra that consists of the primary cohomology operations‎, ‎denoted by $Sq^n$‎, ‎between the cohomology groups with $\mathbb{Z}_2$ coefficients of any topological space‎. ‎Regarding to its vector space structure over $\mathbb{Z}_2$‎, ...  Read More