How Is the Adjoint Boundary Operator Defined in Simplicial Complexes?

[wofsy]

If one has a simplicial complex how does one define the adjoint boundary operator from C_k into C_k+1?

This is an alternative to defining cohomology in terms of the dual space.

 

[wofsy]

If one has a simplicial complex how does one define the adjoint boundary operator from C_k into C_k+1?

This is an alternative to defining cohomology in terms of the dual space.

I see how to do this. Just take the transpose.