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Yayın Higher analogues of discrete topological complexity(Cornell Univ, 2024-04-16) Alabay, Hilal; Borat, Ayşe; Cihangirli, Esra; Erdal, Esma DiricanIn this paper, we introduce the n−th discrete topological complexity and study its properties such as its relation with simplicial LusternikSchnirelmann category and how the higher dimensions of discrete topological complexity relate with each other. Moreover, we find a lower bound of n−discrete topological complexity which is given by the n−th usual topological complexity of the geometric realisation of that complex. Furthermore, we give an example for the strict case of that lower bound.Yayın On twisted torsion of compact 3-manifolds(Cornell Univ, 2024-08-20) Erdal, Esma DiricanLet M be a 3-manifold with connected non-vacuos boundary which is not spherical. Assume that N is another 3-manifold with vacuous boundary and N∗ is the 3-manifold obtained by removing from N the interior of a 3-cell. In the present paper, we find a relationship between the multiplicative property of the twisted Reidemeister torsion and the connected sum operation on these manifolds in order to understand their topology and geometry.
