S. Avvakumov

activity

20122023

most citedAny cyclic quadrilateral can be inscribed in any closed convex smooth curve

18 citations · 63 across the 14 of their papers we have counts for

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6 papers · 1 filter

math.GT2019

Vanishing of all equivariant obstructions and the mapping degree

Sergey Avvakumov, Sergey Kudrya

Suppose that $n \neq = p^{k}$ and $n \neq = 2 p^{k}$ for all $k$ and all primes $p$ . We prove that for any Hausdorff compactum $X$ with a free action of the symmetric group $S_{n}$ th…

math.GT2019★ 1 cited

Stronger counterexamples to the topological Tverberg conjecture

S. Avvakumov, R. Karasev, A. Skopenkov

Denote by $Δ_{M}$ the $M$ -dimensional simplex. A map $f : Δ_{M} \to R^{d}$ is an almost $r$ -embedding if $f σ_{1} \cap \dots \cap f σ_{r} = \emptyset$ whenever $σ_{1}, \dots, σ_{r}$ are pairw…

math.GT2017

The classification of linked $3$ -manifolds in $6$ -space

Sergey Avvakumov

Let $M_{1}$ and $M_{2}$ be closed connected orientable $3$ -manifolds. We classify the sets of smooth and piecewise linear isotopy classes of embeddings $M_{1} ⊔ M_{2} \to S^{6}$ .

math.GT2015★ 10 cited

Eliminating Higher-Multiplicity Intersections, III. Codimension 2

S. Avvakumov, I. Mabillard, A. Skopenkov +1

We study conditions under which a finite simplicial complex $K$ can be mapped to $R^{d}$ without higher-multiplicity intersections. An almost $r$ -embedding is a map $f: K\to…

math.GT2014

The classification of certain linked $3$ -manifolds in $6$ -space

Sergey Avvakumov

We work entirely in the smooth category. An embedding $f : (S^{2} \times S^{1}) ⊔ S^{3} \to R^{6}$ is {\it Brunnian}, if the restriction of $f$ to each component is isoto…

math.GT2012★ 1 cited

How do curved spheres intersect in 3-space?

Sergey Avvakumov

The following problem was proposed in 2010 by S. Lando. Let $M$ and $N$ be two unions of the same number of disjoint circles in a sphere. Do there always exist two spheres in 3-spa…

Vanishing of all equivariant obstructions and the mapping degree

Stronger counterexamples to the topological Tverberg conjecture

The classification of linked 3-manifolds in 6-space

Eliminating Higher-Multiplicity Intersections, III. Codimension 2

The classification of certain linked 3-manifolds in 6-space

How do curved spheres intersect in 3-space?

The classification of linked $3$ -manifolds in $6$ -space

The classification of certain linked $3$ -manifolds in $6$ -space