71 citations · 274 across the 45 of their papers we have counts for
59 papers
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…
Embedding of Higson compactification into the product of adelic solenoids
Alexander Dranishnikov, James Keesling
The Higson compactification of any simply connected proper geodesic metric space admits an embedding into a product of adelic solenoids that induces an isomorphism of 1-dimensional…
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…
Positive scalar curvature and strongly inessential manifolds
Alexander Dranishnikov
We prove that a closed -manifold with positive scalar curvature and abelian fundamental group admits a finite covering which is strongly inessential. The latter means t…
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…