On the fundamental group of the complement of linear torus curves of maximal contact

TL;DR

This paper computes the fundamental group of the complement of linear torus curves with maximal contact and demonstrates its isomorphism to that of generic linear torus curves, revealing topological invariance.

Contribution

It provides the first explicit computation of the fundamental group for these specific torus curves and establishes their topological equivalence to generic cases.

Findings

Fundamental group of the complement is computed.

Shows isomorphism with the fundamental group of generic linear torus curves.

Reveals topological invariance of these curves.

Abstract

In this paper, we compute the fundamental group of the complement of linear torus curves of maximal contact and we show that it is isomorphic that of generic linear torus curves.