# On osculating framing of real algebraic links

## TL;DR

This paper establishes a relationship between the maximal encomplexed writhe and the maximal self-linking number with respect to osculating plane framing in real algebraic links, linking geometric and topological invariants.

## Contribution

It proves that the maximal encomplexed writhe corresponds exactly to the maximal self-linking number with osculating plane framing for real algebraic links.

## Key findings

- Maximal encomplexed writhe is characterized by maximal self-linking number.
- The osculating plane framing plays a key role in understanding link invariants.
- The result connects algebraic, geometric, and topological properties of real algebraic links.

## Abstract

For a real algebraic link in $RP^3$, we prove that its encomplexed writhe (an invariant introduced by Viro) is maximal for a given degree and genus if and only if its self-linking number with respect to the framing by the osculating planes is maximal for a given degree.