Zobrazeno 1 - 10
of 44
pro vyhledávání: '"Avvakumov, Sergey"'
We investigate the dependence on the dimension in the inequalities that relate the volume of a closed submanifold $M^n\subset \mathbb{R}^N$ with its $l^\infty$-width $W^{l^\infty}_{n-1}(M^n)$ defined as the infimum over all continuous maps $\phi:M^n\
Externí odkaz:
http://arxiv.org/abs/2402.07810
We prove the following result: For each closed $n$-dimensional manifold $M$ in a (finite or infinite-dimensional) Banach space $B$, and each positive real $m\leq n$ there exists a pseudomanifold $W^{n+1}\subset B$ such that $\partial W^{n+1}=M^n$ and
Externí odkaz:
http://arxiv.org/abs/2304.02709
Autor:
Avvakumov, Sergey, Karasev, Roman
We prove that if an $n$-dimensional space $X$ satisfies certain topological conditions then any triangulation of $X$ as well as any its representation as a simplicial set with contractible faces has at least $2^n$ faces of dimension $n$. One example
Externí odkaz:
http://arxiv.org/abs/2110.03556
Inspired by the classical Riemannian systolic inequality of Gromov we present a combinatorial analogue providing a lower bound on the number of vertices of a simplicial complex in terms of its edge-path systole. Similarly to the Riemannian case, wher
Externí odkaz:
http://arxiv.org/abs/2106.10429
Autor:
Avvakumov, Sergey, Karasev, Roman
We prove that, for any positive integer $m$, a segment may be partitioned into $m$ possibly degenerate or empty segments with equal values of a continuous function $f$ of a segment, assuming that $f$ may take positive and negative values, but its val
Externí odkaz:
http://arxiv.org/abs/2009.09862
We address a long-standing and long-investigated problem in combinatorial topology, and break the exponential barrier for triangulations of real projective space, constructing a trianglation of $\mathbb{RP}^n$ of size $e^{(\frac{1}{2}+o(1))\sqrt{n}{\
Externí odkaz:
http://arxiv.org/abs/2009.02703
Autor:
Avvakumov, Sergey, Kudrya, Sergey
Publikováno v:
Discrete & Computational Geometry (2021): 1-15
Suppose that $n\neq p^k$ and $n\neq 2p^k$ for all $k$ and all primes $p$. We prove that for any Hausdorff compactum $X$ with a free action of the symmetric group $\mathfrak S_n$ there exists an $\mathfrak S_n$-equivariant map $X \to {\mathbb R}^n$ wh
Externí odkaz:
http://arxiv.org/abs/1910.12628
Autor:
Avvakumov, Sergey, Nivasch, Gabriel
We define and study a discrete process that generalizes the convex-layer decomposition of a planar point set. Our process, which we call "homotopic curve shortening" (HCS), starts with a closed curve (which might self-intersect) in the presence of a
Externí odkaz:
http://arxiv.org/abs/1909.00263
Autor:
Avvakumov, Sergey, Karasev, Roman
Publikováno v:
Mathematika 67:1 (2020), 36--53
In this paper we study envy-free division problems. The classical approach to such problems, used by David Gale, reduces to considering continuous maps of a simplex to itself and finding sufficient conditions for this map to hit the center of the sim
Externí odkaz:
http://arxiv.org/abs/1907.11183
Autor:
Fulek, Radoslav, Avvakumov, Sergey
In the picture-hanging puzzle we are to hang a picture so that the string loops around $n$ nails and the removal of any nail results in a fall of the picture. We show that the length of a sequence representing an element in the free group with $n$ ge
Externí odkaz:
http://arxiv.org/abs/1812.06335