Oleg Viro
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View article: Rokhlin's signature theorems
Rokhlin's signature theorems Open
This note is written for a book dedicated to outstanding St-Petersburg mathematicians and timed to the ICM-2022 in St-Petersburg. In accordance with the plan of ICM-organizers, we try to tell about one of the most prominent Rokhlin's achie…
View article: Fundamental group in the projective knot theory
Fundamental group in the projective knot theory Open
In this paper, properties of a link $L$ in the projective space $\mathbb R P^3$ are related to properties of its group $π_1(\mathbb R P^3\smallsetminus L)$: $L$ is isotopic to a projective line if and only if $π_1(\mathbb R P^3\smallsetmin…
View article: Choreography of divisors on algebraic curves
Choreography of divisors on algebraic curves Open
For a non-singular real algebraic projective curve, topological restrictions on a closed motion of a simple real divisor in its linear equivalence class are found.
View article: Characterization of affine links in the projective space
Characterization of affine links in the projective space Open
A projective link is a smooth closed 1-submanifold of the real projective space of dimension three. A projective link is said to be affine if it is isotopic to a link, which does not intersect some projective plane. The main result: a proj…
View article: Space of Smooth 1-Knots in a 4-Manifold: Is Its Algebraic Topology Sensitive to Smooth Structures?
Space of Smooth 1-Knots in a 4-Manifold: Is Its Algebraic Topology Sensitive to Smooth Structures? Open
We discuss a possibility to get an invariant of a smooth structure on a closed simply connected 4-manifold from homotopy invariants of the space of loops smoothly embedded into the manifold.