Chain-level equivariant string topology: algebra versus analysis

Abstract

We prove that on 2-connected closed oriented manifolds, the analytic and algebraic constructions of an IBL${}_{\infty }$ structure associated to a closed oriented manifold coincide. The corresponding structure is invariant under orientation preserving homotopy equivalences and induces on homology the involutive Lie bialgebra structure of Chas and Sullivan.

Title changed from "Chain-level equivariant string topology for simply connected manifolds". 45p