45 citations · 175 across the 43 of their papers we have counts for
8 papers · 1 filter
Cohomological dimension, self-linking, and systolic geometry
Alexander N. Dranishnikov, Mikhail G. Katz, Yuli B. Rudyak
Given a closed manifold M, we prove the upper bound of (n+d)/2 for the length of a product of systoles that can form a curvature-free lower bound for the total volume of M, in the…
Systolic invariants of groups and 2-complexes via Grushko decomposition
Yuli B. Rudyak, Stéphane Sabourau
We prove a finiteness result for the systolic area of groups, answering a question of M. Gromov. Namely, we show that there are only finitely many possible unfree factors of fundam…
Systoles of 2-complexes, Reeb graph, and Grushko decomposition
Mikhail G. Katz, Yuli B. Rudyak, Stephane Sabourau
Let X be a finite 2-complex with unfree fundamental group. We prove lower bounds for the area of a metric on X, in terms of the square of the least length of a noncontractible loop…
Lusternik-Schnirelmann category and systolic category of low dimensional manifolds
Mikhail G. Katz, Yuli B. Rudyak
We show that the geometry of a Riemannian manifold (M,g) is sensitive to the apparently purely homotopy-theoretic invariant of M known as the Lusternik-Schnirelmann category, denot…
A remark on fixed point sets of gradient-like flows
Yuli Rudyak
Let be a set of critical points of a smooth real-valued function on a closed manifold . Generalizing a well-known result of Lusternik--Schnirelmann, Reeken~[R] proved that $…
On symplectic manifolds with aspherical symplectic form
Yuli Rudyak, Aleksy Tralle
We consider closed symplectically aspherical manifolds, i.e. closed symplectic manifolds satisfying the condition . Rudyak and Oprea [RO] remarked that such…
On Thom spaces, Massey products and non-formal symplectic manifolds
Yuli Rudyak, Aleksy Tralle
In this work we analyze the behavior of Massey products of closed manifolds under the blow-up construction. The results obtained in the article are applied to the problem of constr…
On strict category weight and Arnold conjecture
Yuli B. Rudyak
In [R2] and [RO] the Arnold conjecture for closed symplectic manifolds with trivial second homotopy group was proved. This proof used surgery and cobordism theory. Here we give a p…