On Homology Groups of a Subspace of Triangulations of the Two-Simplex with not More than 6 Subdivisional Boundary Vertices

We study homology groups of the space $\tilde W_1(\nabla^N)$ of triangulations of the two-dimensional simplex with vertices $D_0D_1D_2$ endowed with a boundary subdivision with not more than $6$ vertices in case when this boundary subdivision is extended to the interior of the simplex without adding new interior vertices. As a result, we obtain a theorem about the homology groups $H_n$ in cases $n=0, \dots, 5$.
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