10 papers
Arboricity and Simplicial Geometric Category of Wedges and Joins of Graphs
Nursultan Kuanyshov, Islam Yeginbay
We investigate the behavior of arboricity under two fundamental graph operations, namely wedges and joins, proving an exact formula for wedges and establishing general upper and lo…
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…
Cohomological dimension of a Lie algebra homomorphism
Nursultan Kuanyshov
We introduce the notions of the cohomological dimension and the homological dimension of Lie algebra homomorphisms, extending the corresponding invariants for group homomorphisms.…
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 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)…
On the LS-category of homomorphism of almost nilpotent groups
Nursultan Kuanyshov
We prove the equality $\cat(ϕ)=\cd(ϕ)$ for epimorphisms between torsion-free, finitely generated almost nilpotent groups and . In addition, we prove the equality…
On the LS-category of homomorphisms of groups with torsion
Nursultan Kuanyshov
We prove the equality $\cat(ϕ)=\cd(ϕ)$ for homomorphisms between finitely generated abelian groups and , where for the torsion subgroups of …
On the LS-category of homomorphisms
Alexander Dranishnikov, Nursultan Kuanyshov
We prove the equality $\cat(ϕ)=\cd(ϕ)$ for homomorphisms of a torsion free finitely generated nilpotent groups to an arbitrary group . We construct an epimorphism…