S. A. Melikhov

collaborators

4 papers

math.LO2025

A joint logic of problems and propositions

Sergey A. Melikhov

In a 1985 commentary to his collected works, Kolmogorov informed the reader that his 1932 paper 'On the interpretation of intuitionistic logic' "was written in hope that with time,…

math.GT2025

Lifting generic maps to embeddings. The double point obstruction

Sergey A. Melikhov

Given a generic PL map or a generic smooth fold map $f : N^{n} \to M^{m}$ , where $m \geq n$ and $2 (m + k) \geq 3 (n + 1)$ , we prove that $f$ lifts to a PL or smooth embedding $N\to M\times\mathbb…

math.GT2025

Local knots and the prime factorization of links

Sergey A. Melikhov

The present note contains a new proof of Y. Hashizume's 1958 theorem that every non-split link in $S^{3}$ admits a unique factorization into prime links. While the new proof does not…

math.GT2025

Topological isotopy and finite type invariants

Sergey A. Melikhov

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 l…