Calculation of Fundamental Groups via Computational Paths
Tiago M. L. Veras, Arthur Ramos, Ruy J. G. B. de Queiroz, A. G. de Oliveira · 2021
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.