83 citations · 542 across the 80 of their papers we have counts for
18 papers · 1 filter
Topological lower bounds on the sizes of simplicial complexes and simplicial sets
Sergey Avvakumov, Roman Karasev
We prove that if an -dimensional space satisfies certain topological conditions then any triangulation of as well as any its representation as a simplicial set with cont…
Envy-free division using mapping degree
Sergey Avvakumov, Roman Karasev
In this paper we study envy-free division problems. The classical approach to such problems, used by David Gale, reduces to considering continuous maps of a simplex to itself and f…
Bisecting measures with hyperplane arrangements
Alfredo Hubard, Roman Karasev
We show that when is a power of two, any measures in can be bisected by an arrangement of hyperplanes.
Orthogonal shadows and index of Grassmann manifolds
Djordje Baralić, Pavle V. M. Blagojević, Roman Karasev +1
In this paper we study the action on real Grassmann manifolds and given by taking (appropriately oriented) orthogonal complemen…
Local multiplicity of continuous maps between manifolds
Pavle V. M. Blagojević, Roman Karasev
Let and be smooth (real or complex) manifolds, and let be equipped with some Riemannian metric. A continuous map admits a local -multipl…
The Schwarz genus of the Stiefel manifold and counting geometric configurations
Pavle Blagojević, Roman Karasev
In this paper we compute: the Schwarz genus of the Stiefel manifold with respect to the action of the Weyl group , and the Lust…