71 citations · 274 across the 45 of their papers we have counts for
24 papers · 1 filter
On topological complexity of hyperbolic groups
Alexander Dranishnikov
We show that the topological complexity of a finitely generated torsion free hyperbolic group with $\cdπ=n$ equals .
On Macroscopic dimension of non-spin 4-manifolds
Michelle Daher, Alexander Dranishnikov
We prove that for 4-manifolds with residually finite fundamental group and non-spin universal covering $\Wi M$, the inequality $\dim_{mc}\Wi M\le 3$ implies the inequality $\di…
The topological complexity and the homotopy cofiber of the diagonal map for non-orientable surfaces
Alexander Dranishnikov
We show that the Lusternik-Schnirelmann category of the homotopy cofiber of the diagonal map for non-orientable surfaces equals three. Also, we prove that the topological complexit…
The LS-category of the product of lens spaces
Alexander Dranishnikov
We reduced Rudyak's conjecture that a degree one map between closed manifolds cannot raise the Lusternik-Schnirelmann category to the computation of the category of the product of…
On Gromov's conjecture for totally non-spin manifolds
Dmitry Bolotov, Alexander Dranishnikov
Gromov's Conjecture states that for a closed -manifold with positive scalar curvature the macroscopic dimension of its universal covering satisfies the inequality…
On Gromov's positive scalar curvature conjecture for virtual duality groups
Alexander Dranishnikov
We prove the inequality $$ \dim_{mc}\Wi M\le n-2$$ for the macroscopic dimension of the universal covers $\Wi M$ of almost spin -manifolds with positive scalar curvature who…