Higher Groupoids of Gauge Potentials in Higher Gauge Theories admitting Weights

Abstract

We construct an explicit small model for the ∞-groupoid of null-concordances of higher gauge curvatures by algorithmically trivializing their nonlinear Bianchi identities. More precisely, for a finite-type Sullivan minimal Bianchi algebra equipped with positive integer weights, we organize weighted potentials and higher gauge parameters at each fixed curvature into an ∞-groupoid whose gauge transformations are linear in the parameters. We prove that this model is naturally equivalent to the ∞-groupoid of null-concordances through an intermediate total-form model, with explicit projection and section maps and simplicial homotopies. When nonempty, its connected components form a torsor for the degree-zero cohomology of an associated weighted gauge complex, and its higher homotopy groups are computed by the higher cohomology of this complex.

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BibTeX RIS

BibTeX

@misc{giotopoulos2026higher,
  title = {{Higher Groupoids of Gauge Potentials in Higher Gauge Theories admitting Weights}},
  author = {Grigorios Giotopoulos},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03064},
  eprint = {2611.03064},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03064},
}

RIS

TY  - UNPB
TI  - Higher Groupoids of Gauge Potentials in Higher Gauge Theories admitting Weights
AU  - Grigorios Giotopoulos
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.03064
UR  - https://arxiv.org/abs/2611.03064
AB  - We construct an explicit small model for the ∞-groupoid of null-concordances of higher gauge curvatures by algorithmically trivializing their nonlinear Bianchi identities. More precisely, for a finite-type Sullivan minimal Bianchi algebra equipped with positive integer weights, we organize weighted potentials and higher gauge parameters at each fixed curvature into an ∞-groupoid whose gauge transformations are linear in the parameters. We prove that this model is naturally equivalent to the ∞-groupoid of null-concordances through an intermediate total-form model, with explicit projection and section maps and simplicial homotopies. When nonempty, its connected components form a torsor for the degree-zero cohomology of an associated weighted gauge complex, and its higher homotopy groups are computed by the higher cohomology of this complex.
ER  -

Abstract

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