# Generalized connected sum formula for the Arnold invariants of generic plane curves

## TL;DR

This paper introduces a generalized connected sum operation for generic closed plane curves, extending Arnold's original sum, and thoroughly analyzes how key Arnold invariants change under this new operation.

## Contribution

It provides a comprehensive description of the behavior of Arnold invariants under the generalized connected sum, expanding the understanding of invariants for plane curves.

## Key findings

- Derived formulas for Arnold invariants under the generalized sum
- Extended Arnold's original sum to a broader class of curves
- Enhanced the theoretical framework for plane curve invariants

## Abstract

We define the generalized connected sum for generic closed plane curves, generalizing the strange sum defined by Arnold, and completely describe how the Arnold invariants $J^{\pm}$ and $\mathit{St}$ behave under the generalized connected sums.

---
Source: https://tomesphere.com/paper/1703.09489