Waist of the sphere for maps to manifolds
We generalize the sphere waist theorem of Gromov and the Borsuk--Ulam type measure partition lemma of Gromov--Memarian for maps to manifolds.
math.MG↗
arXiv subjects
A. Yu. Volovikov
Publications and source records attributed to A. Yu. Volovikov.
Configuration-like spaces and coincidences of maps on orbits
In this paper we study the spaces of $q$-tuples of points in a Euclidean space, without $k$-wise coincidences (configuration-like spaces). A transitive group action by permuting these points is considered, and some new upper bounds on the genus (in the sense of Krasnosel'skii--Schwarz and Clapp--Puppe) for this action are given. Some theorems of Cohen--Lusk type for coincidence points of continuous maps to Euclidean spaces are deduced.
math.AT↗
Knaster's problem for almost $(Z_p)^k$-orbits
In this paper some new cases of Knaster's problem on continuous maps from spheres are established. In particular, we consider an almost orbit of a $p$-torus $X$ on the sphere, a continuous map $f$ from the sphere to the real line or real plane, and show that $X$ can be rotated so that $f$ becomes constant on $X$.
math.AT↗