An alternative approach to the calculation of fundamental groups based on labeled natural deduction
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In this work, we use a labelled deduction system based on the concept of computational paths (sequence of rewrites) as equalities between two terms of the same type. We also define a term rewriting system that is used to make computations between these computational paths, establishing equalities between equalities. We use a labelled deduction system based on the concept of computational paths (sequence of rewrites) to obtain some results of algebraic topology and with support of the Seifet-Van Kampen Theorem we will calculate, in a way less complex than the one made in mathematics Munkres and the technique of homotopy type theory hott, the fundamental group of Klein Blottle K^2, of the Torus T^2 and Two holed Torus M_2=T^2#T^2 (the connected sum two torus).
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