3 citations · 4 across the 7 of their papers we have counts for
7 papers
Short proof of the Kneser-Edmonds theorem on the degree of a map between closed surfaces
Andrey Ryabichev
Suppose for closed surfaces there exists a continuous map of geometric degree . Then . This inequality was first proved by Kneser in case…
Maximal degree of a map of surfaces
Andrey Ryabichev
Given closed possibly nonorientable surfaces , we prove that if a map has degree , then . We give all necessary comments on the definition…
Immersions of manifolds
Andrey Ryabichev
This text is based on my talk at the popular science conference ``Dark geometry fest'' which was related to geometric methods and their applications, July 17, 2022. We will move to…
Cutting a triangle into equal triangles
Andrey Ryabichev
We prove that almost every triangle can be dissected only into triangles which have to be equal one another. Moreover, such a dissection is unique for every . It turns out…
Motivated exposition of the proof of the Tverberg Theorem
V. Retinskiy, A. Ryabichev, A. Skopenkov
We present a motivated exposition of the proof of the following Tverberg Theorem: For every integers any points in can be decomposed into gro…
Maps of manifolds of the same dimension with prescribed Thom-Boardman singularities
Andrey Ryabichev
In this paper we extend Y.Eliashberg's -principle to arbitrary generic smooth maps of smooth manifolds. Namely, we prove a necessary and sufficient condition for a continuous ma…
Eliashberg's -principle and generic maps of surfaces with prescribed singular locus
Andrey Ryabichev
We extend Y.Eliashberg's -principle to smooth maps of surfaces which are allowed to have cusp singularities, as well as folds. More precisely, we prove a necessary and sufficien…