Tane Vergili Articles List

List of Articles Tane Vergili

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1 - A note on the new basis in the mod 2 Steenrod algebra
T. Vergili I. Karaca
20.1001.1.22520201.2018.07.02.3.8

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

&lrm;The Mod $2$ Steenrod algebra is a Hopf algebra that consists of the primary cohomology operations&lrm;, &lrm;denoted by $Sq^n$&lrm;, &lrm;between the cohomology groups with $\mathbb{Z}_2$ coefficients of any topological space&lrm;. &lrm;Regarding to its vector space structure over $\mathbb{Z}_2$&lrm;, &lrm;it has many base systems and some of the base systems can also be restricted to its sub algebras&lrm;. &lrm;On the contrary&lrm;, &lrm;in addition to the work of Wood&lrm;, &lrm;in this paper we define a new base system for the Hopf subalgebras $\mathcal{A}(n)$ of the mod $2$ Steenrod algebra which can be extended to the entire algebra&lrm;. &lrm;The new base system is obtained by defining a new linear ordering on the pairs $(s+t,s)$ of exponents of the atomic squares $Sq^{2^s(2^t-1)}$ for the integers $s\geq 0$ and $t\geq 1$&lrm;. Manuscript profile
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2 - Invariant elements in the dual Steenrod algebra
T. Vergili I. Karaca
20.1001.1.22520201.2019.08.03.2.6

&lrm;In this paper&lrm;, &lrm;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 $(\chi-1)({\mathcal{A}_p}^*)_d$&lrm;, &lrm;where $({\mathcal{A}_p}^*)_d$ More

&lrm;In this paper&lrm;, &lrm;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 $(\chi-1)({\mathcal{A}_p}^*)_d$&lrm;, &lrm;where $({\mathcal{A}_p}^*)_d$ is the dimension of ${\mathcal{A}_p}^*$ in degree $d$&lrm;. Manuscript profile
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3 - Conjectures on the anti-automorphism of Z-basis of the Steenrod algebra
T. Vergili I. Karaca
20.1001.1.22520201.2021.10.01.2.6

In this paper, we compute the images of some of the $Z$-basis elements under the anti-automorphism map $\chi$ of the mod 2 Steenrod algebra $\mathcal{A}_2$ and propose some conjectures based on our computations.

In this paper, we compute the images of some of the $Z$-basis elements under the anti-automorphism map $\chi$ of the mod 2 Steenrod algebra $\mathcal{A}_2$ and propose some conjectures based on our computations. Manuscript profile
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4 - Topological spaces induced by homotopic distance
T. Vergili A. Borat
10.30495/jlta.2022.1955292.1482

20.1001.1.22520201.2022.11.02.2.5

&lrm;Topological complexity which plays an important role in motion planning problem can be generalized to homotopic distance $\mathrm{D}$ as introduced in \cite{MVML}&lrm;. &lrm;In this paper&lrm;, &lrm;we study the homotopic distance and mention that it can be realize More

&lrm;Topological complexity which plays an important role in motion planning problem can be generalized to homotopic distance $\mathrm{D}$ as introduced in \cite{MVML}&lrm;. &lrm;In this paper&lrm;, &lrm;we study the homotopic distance and mention that it can be realized as a pseudometric on $\mathrm{Map}(X,Y)$&lrm;. &lrm;Moreover we study the topology induced by the pseudometric $\mathrm{D}$&lrm;. &lrm;In particular&lrm;, &lrm;we consider the space $\mathrm{Map}(S^1,S^1)$ and use the non-compactness of it to talk about the non-compactness of $\mathrm{Map}(X,Y)$&lrm;. Manuscript profile

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List of Articles Tane Vergili