Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4661488 | Topology and its Applications | 2006 | 37 Pages |
Abstract
For an orbifold M we define a new homology group, called t-singular homology group t-Hq(M) by using singular simplicies intersecting ‘transversely’ with ΣM. The rightness of this homology group is ensured by the facts that the 1-dimensional homology group t-H1(M) is isomorphic to the abelianization of the orbifold fundamental group π1(M,x0). If M is a manifold, t-Hq(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.
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