Signed dual graphs and face spectral gaps of Cayley 2-complexes

@misc{hua2026signed,
  title = {{Signed dual graphs and face spectral gaps of Cayley 2-complexes}},
  author = {Bobo Hua and Yong Lin and Tao Wang and Haohang Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22916},
  eprint = {2610.22916},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22916},
}

TY  - UNPB
TI  - Signed dual graphs and face spectral gaps of Cayley 2-complexes
AU  - Bobo Hua
AU  - Yong Lin
AU  - Tao Wang
AU  - Haohang Zhang
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.22916
UR  - https://arxiv.org/abs/2610.22916
AB  - We construct a weighted signed dual multigraph for the Cayley $2$-complex of a finite presentation and represent its ℓ^2 face Laplacian as a signed graph Laplacian with a diagonal potential. We prove that the face spectral gap above the kernel vanishes for the Baumslag--Solitar groups BS(1,m), m≥2, using explicit finitely supported face chains. Our main vanishing theorem gives the same conclusion for every finitely presented amenable group with ordinary first Betti number at least two.
ER  -