Se p 20 05 The homotopy invariance of the string topology loop product and string bracket

Let M be a closed, oriented, n-manifold, and LM its free loop space. In [3] a commutative algebra structure in homology, H∗(LM), and a Lie algebra structure in equivariant homology H 1 ∗ (LM), were defined. In this paper we prove that these structures are homotopy invariants in the following sense. Let f : M1 → M2 be a homotopy equivalence of closed, oriented n-manifolds. Then the induced equivalence, Lf : LM1 → LM2 induces a ring isomorphism in homology, and an isomorphism of Lie algebras in equivariant homology. The analogous statement also holds true for any generalized homology theory h∗ that supports an orientation of the Mi’s.