Homology Groups of Trisps with Integer Coefficients

3 Homology Groups of Trisps with Integer Coefficients 

We shall now combine the orientations of Subsection 3.2.2 with the algebraic procedure of Subsection 3.2.1. 

Let A be an arbitrary trisp, with the standard orientation on its simplices. For n 0, let Cn A) denote the free abelian group generated by the oriented simplices of A of dimension n, that is. 

In line with the previous terminology, a linear combination is called an n-chain with integer coefficients, and the group C (Z ) is called an n-chain group with integer coefficients. 

Just as in previous cases, one can define the boundary operator, which this time is an abelian group homomorphism 

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