TITLE: Griffiths and Harris reference
QUESTION [19 upvotes]: Trying to read the section on Poincare duality from Griffiths and Harris is a nightmare. I want to know if there is a place where Poincare duality and intersection theory are done cleanly and rigorously in the order that GH do them (usually, one proves Poincare duality for singular cohomology and then defines the intersection pairing by cup product and proves that (using the Thom isomorphism) that indeed the intersection pairing counts the number of points taken with sign (and convert everything to forms using De Rham's theorem). GH on the other hand define intersection pairing and then proceed further. However, one has to wave their hands at relativistic speeds to make some things work here).

REPLY [5 votes]: I ran into the same problem with G&H treatment of Poincare duality. It seems incomplete, for example they refer to "cells" without defining that term. Following the suggestion from one of the comments above I turned to Seifert and Threlfall and I did find it to be a good source to fill in the missing pieces of the G&H approach. Having studied homology from the singular point of view (Massey) I found the simplicial approach of S&T enlightening.