The Low Bound Of Homeomorphic Class In K_n Graphlike Manifolds

K_n is 1-skeletonof n-simplex, that is, K_n is a complete graph with n vertices.A K_n graphlike manifold M is a quotient space X/～, andin which (z,0)? f_ijⁱ(z,0), (z,1)?f_ij^j(z,1)if z∈S_ij¹,where S_i¹ and S_ij¹ are circles, and the adjunction mapsare homeomorphic.A K_n graphlike manifold is correspond to an n- matrix (a_ij), in which the elements of its diagonal are 0, and its otherelements are defined bysince the mapping degree of homeomorphic map is 1 or -1. The matrix (a_ij) is called the associated matrix of K_n graphlikemanifold.In this thesis, we show that the characteristic polynomial |λI-(a_ij)| of associated matrix and the permanent Per(a_ij) are twotopological invariants of K_n graphlike manifold. By using the two topological invariants, the low bounds of homeomorphic...