Ringing the eigenmodes from compact manifolds

Surgery on Compact Manifolds

Volumes of Compact Manifolds

We present a systematic calculation of the volumes of compact manifolds which appear in physics: spheres, projective spaces, group manifolds and generalized flag manifolds. In each case we state what we believe is the most natural scale or normalization of the manifold, that is, the generalization of the unit radius condition for spheres. For this aim we first describe the manifold with some pa...

Computation of eigenmodes on a compact hyperbolic space

Measurements of CMB anisotropy are ideal experiments for discovering the non-trivial global topology of the universe. To evaluate the CMB anisotropy in multiply-connected(MC) compact cosmological models, one needs to compute the eigenmodes of the Laplace-Beltrami operator. We numerically obtain the low-lying eigenmodes on a compact 3-hyperbolic space called m003(−2, 3) in the SnapPea using the ...

Exact Polynomial Eigenmodes for Homogeneous Spherical 3-Manifolds

Observational data hint at a finite universe, with spherical manifolds such as the Poincaré dodecahedral space tentatively providing the best fit. Simulating the physics of a model universe requires knowing the eigenmodes of the Laplace operator on the space. The present article provides explicit polynomial eigenmodes for all globally homogeneous 3-manifolds: the Poincaré dodecahedral space S3/...

Low-lying Dirac eigenmodes and monopoles in 4D compact QED

We study the correlations between the fluctuations of low-lying Dirac eigenfunctions and monopoles in quenched compact QED at β=0.99, 1.01 and 1.03, employing 12 × 12 lattices and the overlap formalism for the fermion action. Near-zero modes are found to have universal anti-correlations with monopoles below/above the critical β. In contrast to the result in QCD by Garcia-Garcia and Osborn, near...