Singular prism operator
= Singular prism operator
{title2=$\partial P+P\partial=g_\#-f_\#$}
Triangulate $\Delta^q\times I$ by the simplices with vertices $(v_0,0),\ldots,(v_i,0),(v_i,1),\ldots,(v_q,1)$ and coefficients $(-1)^i$. Composing with a <homotopy> between f and g gives a degree-one map P on <singular chains>. Shared faces cancel; the remaining faces give the displayed <chain homotopy> identity. Hence homotopic maps induce the same map on <singular homology>.