2009/07/09 by J. S. Dowker, Dowker, J. S.
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric and Algebraic Topology #Group Theory (math.GR) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #gr-qc #hep-th #math-ph #math.DG #math.GR #math.MP
paper · pdf · doi:10.48550/arxiv.0907.1309
14 pages
arxiv created 2009/07/09 · openalex publication_date 2009/07/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Ray-Singer isospectral theorem (1971) is applied to a general spectral function for Laplacians of twisted p-forms (say) on homogeneous Clifford-Klein factors of the three-sphere. The inducing formulae necessary to express any spectral quantity for any twisting in terms of those for cyclic subgroups of the tetrahedral, octahedral and icosahedral deck groups are detailed. Further, Artin's theorem allows the McKay correspondence to be obtained. The isospectral theorem is shown to yield a derivation of the Sunada construction which is equivalent to the later one by Pesce.