The spinor bundle on loop space

2023/05/21 by Matthias Ludewig, Ludewig, Matthias
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2305.12521

openalex publication_date 2023/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a construction of the spinor bundle of the loop space of a string manifold together with its fusion product, inspired by ideas from Stolz and Teichner. The spinor bundle is a super bimodule bundle for a bundle of Clifford von Neumann algebras over the free path space, and the fusion product is defined using Connes fusion of such bimodules. As the main result, we prove that a spinor bundle with fusion product on a manifold X exists if and only X admits a string structure.

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