Recent content by sanad

@WWGD, can i take the map:# pci:R→S1# for my qeustion" find an example of #ψ: C•→D•# co-chain map that exists : #ψi:Ci→Di# is an surjective map (for i>=0) but #ψ∗: (H^k)(C•)→(H^k)D•)# is not a surjective map (for k>=0)? I want to check if an identity map or # pci:R→S1# map can be an example of...

prove that if ##g:Y→Z## and ##f:X→Y## are two smooth maps between a smooth manifolds, then a homomorphism that induced are fulfilling :## (g◦f)∗=f∗◦g∗\, :\, H∙(Z)→H∙(X)## I must to prove this by a differential forms, but I do not how I can use them . I began in this way: if f∗ : H(Y)→H(X), g∗...