6 papers · 1 filter
Sequential -contiguity distance
Nilay Ekiz Yazici, Nursultan Kuanyshov, Ayse Borat
In this paper, we introduce the notion of sequential -contiguity distance for finitely many simplicial maps as a higher analogue of contiguity distance. This invariant generaliz…
m-Contiguity Distance
Nilay Ekiz Yazici, Nursultan Kuanyshov, Ayse Borat
In this paper, we systematically develop the -contiguity distance between simplicial maps as a discrete approximation framework for homotopical complexity in the category of sim…
Small Value of cohomological dimension of group homomorphisms
Nursultan Kuanyshov
We give the characterisation of cohomological dimension of group homomorphisms. In particular, we show the analogue of the Stallings-Swan theorem in the case of group epimorphisms.
On numerical invariants of retraction map
Nursultan Kuanyshov
We introduce a notion of retraction between continuous maps of topological spaces and study the behavior of several numerical invariants under such retractions. These include (co)h…
On the LS-category of homomorphisms of groups with torsion
Nursultan Kuanyshov
We prove the equality $\cat(Ï)=\cd(Ï)$ for homomorphisms between finitely generated abelian groups and , where for the torsion subgroups $T(Î…
On the sequential topological complexity of group homomorphisms
Nursultan Kuanyshov
We define and develop a homotopy invariant notion for the sequential topological complexity of a map denoted , that interacts with and $TC_{r}(Y)…