Open AccessCalculation of Fundamental Groups via Computational Paths
Author(s) -
Tiago Mendonça Lucena de Veras,
Arthur Ramos,
Ruy J. G. B. de Queiroz,
Anjolina Grisi de Oliveira
Publication year - 2021
Language(s) - English
Resource type - Conference proceedings
DOI - 10.5753/etc.2021.16370
Subject(s) - rewriting , computation , computer science , term (time) , computational geometry , theoretical computer science , torus , computational complexity theory , type (biology) , algebra over a field , mathematics , algorithm , pure mathematics , programming language , geometry , ecology , physics , quantum mechanics , biology
We address the question as to how to formalise the concept of computational paths (sequences of rewrites) as equalities between two terms of the same type. The intention is to demonstrate the use of a term rewriting system in performing computations with these computational paths, establishing equalities between equalities, and further higher equalities, in particular, in the calculation of fundamental groups of surfaces such as the circle, the torus and the real projective plane.