On the number of branches of real curve singularities

TL;DR

This paper introduces a method to compute the number of branches of real analytic curve singularities and the half-branches of double points in specific analytic germs, aiding in understanding their local structure.

Contribution

It presents a novel computational approach for determining branch counts of real curve singularities and double point structures in analytic germs.

Findings

Method effectively computes branch numbers at singular points.

Applicable to real analytic curves from R^n to R^m with m ≥ n.

Provides insights into the local topology of real curve singularities.

Abstract

There is presented a method for computing the number of branches of a real analytic curve germ from $R^n$ to $R^m$, where m is greater or equal to n, having a singular point at the origin, and the number of half--branches of the set of double points of an analytic germ from $R^2$ to $R^3$.