The Chern-Gauss-Bonnet Theorem via supersymmetric Euclidean field theories

2013/10/20 by Daniel Berwick-Evans, Berwick-Evans, Daniel · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Relativity and Gravitational Theory

paper · pdf · doi:10.48550/arxiv.1310.5383

openalex publication_date 2013/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the Chern-Gauss-Bonnet Theorem using sigma models whose source supermanifolds have super dimension 0|2. Along the way we develop machinery for understanding manifold invariants encoded by families of 0|n-dimensional Euclidean field theories and their quantization.

Cited by

• Atiyah class of DG manifolds of positive amplitude
• Intrinsic Parameterization of Supermanifold Morphisms from ℝ^0|2 via Decomposable Bivector Bundles

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