45 citations · 69 across the 8 of their papers we have counts for
8 papers
Rudyak's conjecture for lower dimensional 1-connected manifolds
Alexander Dranishnikov, Deep Kundu
Rudyak's conjecture states that for any degree one map between oriented closed manifolds there is the inequality $\cat (M)\ge \cat(N)$ for the Lusternik-Shnirelmann cate…
On Gromov's conjecture for right-angled Artin groups
Alexander Dranishnikov, Satyanath Howladar
We prove that the universal covering $\Wi M$ of an -dimensional closed spin PSC manifold whose fundamental group is a right-angled Artin group has macroscopic dimen…
On the Lusternik-Schnirelmann category of spaces with 2-dimensional fundamental group
A. Dranishnikov
The following inequality \cat X\le \cat Y+\lceil\frac{hd(X)-r}{r+1}\rceil holds for every locally trivial fibration between spaces which admits a section and has t…
An etale approach to the Novikov conjecture
A. Dranishnikov, S. Ferry, S. Weinberger
We show that the rational Novikov conjecture for a group of finite homological type follows from the mod 2 acyclicity of the Higson compactifcation of an E. We then show tha…
A Hurewicz-type theorem for asymptotic dimension and applications to geometric group theory
G. C. Bell, A. N. Dranishnikov
We prove an asymptotic analog of the classical Hurewicz theorem on mappings which lower dimension. This theorem allows us to find sharp upper bound estimates for the asymptotic dim…
Universal spaces for asymptotic dimension
A. Dranishnikov, M. Zarichnyi
We construct a universal space for the class of proper metric spaces of bounded geometry and of given asymptotic dimension. As a consequence of this result, we establish coincidenc…