arXiv subjects

Nilay Ekiz Yazici

Publications and source records attributed to Nilay Ekiz Yazici.

3 recordsLinked to original sources

arXiv2026

m-Contiguity Distance

In this paper, we systematically develop the $m$-contiguity distance between simplicial maps as a discrete approximation framework for homotopical complexity in the category of simplicial complexes. We construct an increasing sequence of invariants that approximate the contiguity distance from below. We prove that $m$-contiguity distance is invariant under strong homotopy equivalence and that $m$-contiguity distance coincides with the usual contiguity distance provided that the dimension of the domain simplicial complex is $m$. The fundamental properties of $m$-contiguity distance are established, including its behaviour under barycentric subdivision, under compositions, and a categorical poduct inequality. As applications of this theory, we define the $m$-simplicial Lusternik-Schnirelmann category and the $m$-discrete topological complexity, proving that each arises naturally as a special case of $m$-contiguity distance. We also showed that $SD_1(φ,ψ)=SD(φ,ψ)$ under some conditions related to aspherical spaces.

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arXiv2026

Sequential $m$-contiguity distance

In this paper, we introduce the notion of sequential $m$-contiguity distance for finitely many simplicial maps as a higher analogue of contiguity distance. This invariant generalizes both higher contiguity distance and $m$-contiguity distance, and provides a combinatorial counterpart of sequential $m$-homotopic distance. We investigate its fundamental properties, including invariance under strong homotopy type, behaviour under compositions, categorical products, and barycentric subdivision. Moreover, we define sequential $m$-discrete topological complexity of simplicial complexes. As applications, we characterise this invariant (along with $m$-simplicial LS category) in terms of sequential $m$-contiguity distance and prove that they are invariants of strong homotopy type. Furthermore, we establish inequalities relating $m$-simplicial LS category and $m$-discrete sequential topological complexity, extending classical results from topological complexity theory to the simplicial and $m$-dimensional setting.

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arXiv2024

Higher Contiguity Distance

In this paper, we introduce the higher analogues of contiguity distance and its relations with simplicial Lusternik-Schnirelmann category and discrete topological complexity. Also we study the effects of geometric realisation and barycentric subdivision in the sense that how the geometric realisation of the simplicial maps and the induced simplicial maps on barycentric subdivisions affects higher contiguity distance.

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