Zobrazeno 1 - 10
of 98
pro vyhledávání: '"Melikhov, Sergey"'
Autor:
Melikhov, Sergey A.
In 1974, D. Rolfsen asked: Is every knot in $S^3$ isotopic (=homotopic through embeddings) to a PL knot or, equivalently, to the unknot? In particular, is the Bing sling isotopic to a PL knot? We show that the Bing sling is not isotopic to any PL kno
Externí odkaz:
http://arxiv.org/abs/2406.09365
Autor:
Melikhov, Sergey A.
In 1974, D. Rolfsen asked: If two PL links in $S^3$ are isotopic (=homotopic through embeddings), then are they PL isotopic? We prove that they are PL isotopic to another pair of links which are indistinguishable from each other by finite type invari
Externí odkaz:
http://arxiv.org/abs/2406.09331
Autor:
Melikhov, Sergey A.
We prove an "abelian, locally compact" Whitehead theorem in fine shape: A fine shape morphism between locally connected finite-dimensional locally compact separable metrizable spaces with trivial $\pi_0$ and $\pi_1$ is a fine shape equivalence if and
Externí odkaz:
http://arxiv.org/abs/2211.11102
Autor:
Melikhov, Sergey A.
In this paper we obtain results indicating that fine shape is tractable and "not too strong" even in the non-locally compact case, and can be used to better understand infinite-dimensional metrizable spaces and their homology theories. We show that e
Externí odkaz:
http://arxiv.org/abs/2211.11101
Autor:
Melikhov, Sergey A.
Locally compact separable metrizable spaces are characterized among all metrizable spaces as those that admit a cofinal sequence $K_1\subset K_2\subset\cdots$ of compact subsets. Their \v{C}ech cohomology is well-understood due to Petkova's short exa
Externí odkaz:
http://arxiv.org/abs/2211.09951
Autor:
Melikhov, Sergey A.
Publikováno v:
J. Topol. Anal., 12:4 (2020), 1041-1046
We use a triple-point version of the Whitney trick to show that ornaments of three orientable $(2k-1)$-manifolds in $\mathbb R^{3k-1}$, $k>2$, are classified by the $\mu$-invariant. A very similar (but not identical) construction was found independen
Externí odkaz:
http://arxiv.org/abs/2210.04016
Autor:
Melikhov, Sergey A.
Publikováno v:
Topol. Methods in Nonlinear Analysis, 60:1 (2022), 185-201
We present a short proof of S. Parsa's theorem that there exists a compact $n$-polyhedron $P$, $n\ge 2$, non-embeddable in $\mathbb R^{2n}$, such that $P*P$ embeds in $\mathbb R^{4n+2}$. This proof can serve as a showcase for the use of geometric coh
Externí odkaz:
http://arxiv.org/abs/2210.04015
Autor:
Melikhov, Sergey A.
We construct a link in the $3$-space that is not isotopic to any PL link (non-ambiently). In fact, there exist uncountably many $I$-equivalence classes of links. The paper also includes some observations on Cochran's invariants $\beta_i$.
Commen
Commen
Externí odkaz:
http://arxiv.org/abs/2011.01409
Autor:
Melikhov, Sergey A.
Publikováno v:
Stud. Sci. Math. Hung., 59:2 (2022), 124-141
We show that if a non-degenerate PL map $f:N\to M$ lifts to a topological embedding in $M\times\mathbb R^k$ then it lifts to a PL embedding in there. We also show that if a stable smooth map $N^n\to M^m$, $m\ge n$, lifts to a topological embedding in
Externí odkaz:
http://arxiv.org/abs/2011.01402
Autor:
Melikhov, Sergey A.
We prove the analogue of the Concordance Implies Isotopy in Codimension $\ge 3$ Theorem for link maps, together with some other its singular analogues. In the case of spherical link maps, a stronger result was independently obtained by P. Teichner (b
Externí odkaz:
http://arxiv.org/abs/1810.08299