71 citations · 274 across the 45 of their papers we have counts for
16 papers · 1 filter
On cohomological dimension of group homomorphisms
Aditya De Saha, Alexander Dranishnikov
The (co)homological dimension of homomorphism is the maximal number such that the induced homomorphism is nonzero for some -module. The following theorems are pro…
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…
On Iwase's manifolds
Alexander Dranishnikov
In ~\cite{Iw2} Iwase has constructed two 16-dimensional manifolds and with LS-category 3 which are counter-examples to Ganea's conjecture: ${\rm cat_{LS}} (M\times S^n)…
Surgery Approach to Rudyak's Conjecture
Alexander Dranishnikov, Jamie Scott
Using the surgery we prove the following: THEOREM. Let be a normal map of degree one between closed manifolds with being -connected, . If satisfi…
The Lusternik-Schnirelmann category of connected sum
Alexander Dranishnikov, Rustam Sadykov
We use the Berstein-Hilton invariant to prove the formula $\cat(M_1\sharp M_2)=\max\{\cat M_1, \cat M_2\}$ for the Lustrnik-Schnirelmann category of the connected sum of closed man…
An upper bound on the LS-category in presence of the fundamental group
Alexander Dranishnikov
We prove that $$ \cat X\le \frac{\cd(π_1(X))+\dim X}{2}$$ for every CW complex where $\cd(π_1(X))$ denotes the cohomological dimension of the fundamental group of . We obtai…