7 citations · 30 across the 11 of their papers we have counts for
8 papers · 1 filter
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…
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 …
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…
Embeddings of non-simply-connected 4-manifolds in 7-space. I. Classification modulo knots
D. Crowley, A. Skopenkov
We work in the smooth category. Let be a closed connected orientable 4-manifold with torsion free , where . Our main result is a complete readily calculable…
Classification of knotted tori
A. Skopenkov
For a smooth manifold denote by the set of smooth isotopy classes of smooth embeddings . A description of the set was known only…