7 citations · 30 across the 11 of their papers we have counts for
10 papers
The band connected sum and the second Kirby move for higher-dimensional links
A. Skopenkov
Let be a link (i.e. an embedding). How does (the isotopy class of) the knot obtained by embedded connected sum of the components of depend…
Short proofs of Tverberg-type theorems for cell complexes
Roman Karasev, Arkadiy Skopenkov
We present short proofs of Tverberg-type theorems for cell complexes by S. Hasui, D. Kishimoto, M. Takeda, and M. Tsutaya. One of them states that for any prime power , any comp…
Simple proofs of estimations of Ramsey numbers and of discrepancy
A. Buchaev, A. Skopenkov
In this expository note we present simple proofs of the lower bound of Ramsey numbers (Erdös theorem), and of the estimation of discrepancy. Neither statements nor proofs require a…
Some `converses' to intrinsic linking theorems
R. Karasev, A. Skopenkov
A low-dimensional version of our main result is the following `converse' of the Conway-Gordon-Sachs Theorem on intrinsic linking of the graph in 3-space: For any integer …
Extendability of simplicial maps is undecidable
A. Skopenkov
We present a short proof of the Čadek-Krčál-Matoušek-Vokřínek-Wagner result from the title (in the following form due to Filakovský-Wagner-Zhechev). For any fixed even there is…
A user's guide to basic knot and link theory
A. Skopenkov
This paper is expository and is accessible to students. We define simple invariants of knots or links (linking number, Arf-Casson invariants and Alexander-Conway polynomials) motiv…