83 citations · 542 across the 80 of their papers we have counts for
6 papers · 2 filters
A topological central point theorem
R. N. Karasev
In this paper a generalized topological central point theorem is proved for maps of a simplex to finite-dimensional metric spaces. Similar generalizations of the Tverberg theorem a…
Extensions of theorems of Rattray and Makeev
Pavle Blagojević, Roman Karasev
We consider extensions of the Rattray theorem and two Makeev's theorems, showing that they hold for several maps, measures, or functions simultaneously, when we consider orthonorma…
The genus and the Lyusternik-Schnirelmann category of preimages
R. N. Karasev
In this paper some axiomatic generalization (function of open subsets) of the relative Lyusternik-Schnirelmann category is considered, incorporating the sectional category and the…
-index of the grassmanian
R. N. Karasev
We study the real Grassmann manifold (of -subspaces in ), and the action of on it by taking the orthogonal complement. The homological index of…
Regular embeddings of manifolds and topology of configuration spaces
R. N. Karasev
For a topological space we study continuous maps such that images of every pairwise distinct points are affinely (linearly) independent. Such maps ar…
Multiplicity of continuous maps between manifolds
R. N. Karasev
We consider a continuous map between two manifolds and try to estimate its multiplicity from below, i.e. find a -tuple of pairwise distinct points $x_1,..., x_q\in M…