Discrete Homotopy of a Closed k-Surface

摘要

Let SC~(ni,li)_ki be a simple closed ki-curve in Z~(ni) with l_i elements, i ∈ {1, 2}. After doing a (3~(n_1+n2)-1)-homotopic thinning of SC~(n1,l1)_k1*SC~n2, l2 _k2 to obtain a closed (3~(n_1+n2)-1) -surface, we calculate the (3~(n_1+n2)-1) -fundamental group of SC~(n1,l1)_k1*SC~n2,l2_k2 by the use of some properties of an )8,3~(n1+n2_-1)-covering.