Zobrazeno 1 - 10
of 47
pro vyhledávání: '"Skopenkov, Arkadiy"'
Autor:
Karasev, Roman, Skopenkov, Arkadiy
We present short proofs of two 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 $r$, any simplicial sphere $X$ of dimension $(d+1)(r-1)-1$, and any continuous
Externí odkaz:
http://arxiv.org/abs/2405.05629
Autor:
Skopenkov, Arkadiy
The procedure to remove double intersections called the Whitney trick is one of the main tools in the topology of manifolds. The analogues of Whitney trick for $r$-tuple intersections were `in the air' since 1960s. However, only recently they were st
Externí odkaz:
http://arxiv.org/abs/1704.00143
Autor:
Skopenkov, Arkadiy, Tancer, Martin
Publikováno v:
Discr. and Comp. Geom. 61:2 (2019), 452-463
A map $f\colon K\to \mathbb R^d$ of a simplicial complex is an almost embedding if $f(\sigma)\cap f(\tau)=\emptyset$ whenever $\sigma,\tau$ are disjoint simplices of $K$. Theorem. Fix integers $d,k\ge2$ such that $d=\frac{3k}2+1$. (a) Assume that $P\
Externí odkaz:
http://arxiv.org/abs/1703.06305
Autor:
Skopenkov, Arkadiy
Publikováno v:
Topology and its Applications, 240 (2018) 259-269
A map $\varphi:K\to R^2$ of a graph $K$ is approximable by embeddings, if for each $\varepsilon>0$ there is an $\varepsilon$-close to $\varphi$ embedding $f:K\to R^2$. Analogous notions were studied in computer science under the names of cluster plan
Externí odkaz:
http://arxiv.org/abs/1609.03727
Autor:
Skopenkov, Arkadiy
In this expository paper we present short simple proofs of Conway-Gordon-Sachs' theorem on intrinsic linking in three-dimensional space, as well as van Kampen-Flores' and Ummel's theorems on intrinsic intersections. The latter are related to nonreali
Externí odkaz:
http://arxiv.org/abs/1402.0658
Autor:
Kaibkhanov, Ashum, Skopenkov, Arkadiy
Publikováno v:
Mat. Prosveschenie, 10 (2006) 176-184
We present short proofs of the transcendence of the Liouville and the Mahler numbers. The first proof is known for a long time, the second proof apparently appeared only in 2002-2003. The proofs are accessible to high-school students.
Comment: 5
Comment: 5
Externí odkaz:
http://arxiv.org/abs/1204.5045
Autor:
Skopenkov, Arkadiy
Publikováno v:
Mat. Prosveschenie, 21 (2017) 197-204
In this expository note we present a proof of the V.A. Vassiliev conjecture on the planarity of graphs with vertices of degree 4 and certain additional structure. Both statement and proof are accessible to high-school students familiar with basic not
Externí odkaz:
http://arxiv.org/abs/1008.4940
Autor:
Crowley, Diarmuid, Skopenkov, Arkadiy
Publikováno v:
Internat. J. Math. 22:6 (2011) 731-757
Let N be a closed, connected, smooth 4-manifold with H_1(N;Z)=0. Our main result is the following classification of the set E^7(N) of smooth embeddings N->R^7 up to smooth isotopy. Haefliger proved that the set E^7(S^4) with the connected sum operati
Externí odkaz:
http://arxiv.org/abs/0808.1795
Autor:
Skopenkov, Arkadiy
Publikováno v:
Topol. Appl. 157 (2010) 2094-2110
We work in the smooth category. Let N be a closed connected n-manifold and assume that m>n+2. Denote by E^m(N) the set of embeddings N -> R^m up to isotopy. The group E^m(S^n) acts on E^m(N) by embedded connected sum of a manifold and a sphere. If E^
Externí odkaz:
http://arxiv.org/abs/math/0512594