After an introduction to the intersection pairing for PL chains, I’ll discuss four main results. Let M be a compact oriented PL manifold, let C∗M be its PL chain complex, and let LM be its free loop space.

1) The domain of the intersection pairing is quasi-isomorphic to the tensor product of

C∗M with itself; similarly for the iterated intersection pairing.

2) C∗M is canonically quasi-isomorphic to an E-infinity chain algebra, by a quasiisomorphism that respects the intersection pairing.

3) The Eilenberg-Moore spectral sequence whose abutment is H∗(LM) is a spectral sequence of Batalin-Vilkovisky algebras, and the operations on the spectral sequence are compatible with the operations on H∗LM defined by Chas and Sullivan.

4) The Chas-Sullivan operations on H∗LM are induced by a chain-level action of the framed little 2-disks operad on a chain complex quasi-isomorphic to the singular chains of LM.