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PreprintCC BY 4.0arXiv

Linking numbers and special differential characters in arithmetic hyperbolic manifolds

  • Mads Bjerge Christensen
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Abstract

We construct non-holomorphic Siegel modular forms whose coefficients encode linking numbers in arithmetic hyperbolic manifolds of simplest type. Our proofs rely on an improved understanding of the transgression forms appearing in Kudla--Millson theory, and along the way we establish some structural properties including in particular their expected current equations.

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Cite

BibTeXRIS
BibTeX
@misc{christensen2026linking,
  title = {{Linking numbers and special differential characters in arithmetic hyperbolic manifolds}},
  author = {Mads Bjerge Christensen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18503},
  eprint = {2610.18503},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18503},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Linking numbers and special differential characters in arithmetic hyperbolic manifolds
AU  - Mads Bjerge Christensen
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18503
UR  - https://arxiv.org/abs/2610.18503
AB  - We construct non-holomorphic Siegel modular forms whose coefficients encode linking numbers in arithmetic hyperbolic manifolds of simplest type. Our proofs rely on an improved understanding of the transgression forms appearing in Kudla--Millson theory, and along the way we establish some structural properties including in particular their expected current equations.
ER  -