50 citations · 182 across the 49 of their papers we have counts for
49 papers
Embeddability of joinpowers, and minimal rank of partial matrices
A. Skopenkov, O. Styrt
A general position map of a -dimensional simplicial complex to a -dimensional manifold (for , of a graph to a surface) is a -embedding if $|fσ\c…
To S. Parsa's theorem on embeddability of joins
A. Skopenkov
The purpose of this short note is to guide a reader to a reliable reference for the following result of S. Parsa: For any there exist simplicial complexes of dimen…
Invariants of embeddings of 2-surfaces in 3-space
A. Skopenkov
Let be a sphere with handles and holes, an embedding, and . We study a simple isotopy invariant of , the Seifert bilinear form $L(f…
A short proof of the Patak-Tancer theorem on non-embeddability of -complexes in -manifolds
E. Kogan, A. Skopenkov
In 2019 P. Patak and M. Tancer obtained the following higher-dimensional generalization of the Heawood inequality on embeddings of graphs into surfaces. We present a short well-str…
A structured proof of Kolmogorov's Superposition Theorem
S. Dzhenzher, A. Skopenkov
We present a well-structured detailed exposition of a well-known proof of the following celebrated result solving Hilbert's 13th problem on superpositions. For functions of 2 varia…
On the Browder-Levine-Novikov embedding theorems
M. Cencelj, D. Repovš, A. Skopenkov
In this survey we present applications of the ideas of complement and neighborhood in the theory embeddings of manifolds into Euclidean space (in codimension at least three). We de…