Equivalence of string and fusion loop-spin structures

Abstract

The importance of the fusion relation of loops was recognized in the context of spin structures on the loop space by Stolz and Teichner and further developed by Waldorf. On a spin manifold M the equivalence classes of `fusive' spin structures on the loop space LM, incorporating the fusion property, strong regularity and reparameterization-invariance, are shown to be in 1-1 correspondence with equivalence classes of string structures on M. The identification is through the affine space of `string' cohomology classes considered by Redden.

47 pages

References in corpus (2)

• Spin structures on loop spaces that characterize string manifolds
• Geometry of Pseudodifferential algebra bundles and Fourier Integral Operators

Cited by in corpus (3)

• String geometry vs. spin geometry on loop spaces
• A model for complex analytic equivariant elliptic cohomology from quantum field theory
• String${}^{\mathbf{c}}$ Structures and Modular Invariants