On the chain-level intersection pairing for PL manifolds

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Let M be a compact oriented PL manifold and let C*M be its PL chain complex. The domain of the chain-level intersection pairing is a subcomplex G of C*M⊗ C*M. We prove that G is a "full" subcomplex, that is, the inclusion of G in C*M ⊗ C*M is a quasi-isomorphism. An analogous result is true for the domain of the iterated intersection pairing. Using this, we show that the intersection pairing gives C*M a structure of partially defined commutative DGA, which in particular implies that C*M is canonically quasi-isomorphic to an E∞ chain algebra. An erratum is attached which corrects sign errors pointed out by Greg Friedman.