i have this from Hatcher's book "Algebric topology"
And i don't understand why $\displaystyle \partial P(\sigma)=\sum_{j\leq i}(-1)^i(-1)^j F\circ (\sigma\times id)|[v_0,...,\widehat{v}_j,...,w_i,...,w_n]+\sum_{j\geq i}(-1)^i(-1)^{j+1} F\circ (\sigma\times id)|[v_0,...,v_i,\widehat{w}_j,...,w_n]$
Plese.
Thank you.
He's just applying the definition and splitting it over two pieces. The first sum is the contribution from the v components (from $\Delta^n$), and the second is running over (is the contribution from) the w components (from I).