The t-singular homology of orbifolds

摘要

For an orbifold M we define a new homology group, called t-singular homology group t-H_q(M) by using singular simplicies intersecting 'transversely' with ΣM. The Tightness of this homology group is ensured by the facts that the 1-dimensional homology group t-H_1 (M) is isomorphic to the abelianization of the orbifold fundamental group π_1 (M, x_0). If M is a manifold, t-H_q (M) coincides with the usual singular homology group. We prove that it is a 'b-homotopy' invariant of orbifolds and develop many algebraic tools for the calculations. Consequently we calculate the t-singular homology groups of several orbifolds.