Orbifold construction of the modes of the Poincaré dodecahedral space

M. Lachièze-Rey (1) , J. Weeks (2)

1 APC - Cosmologie
2 Topology

We provide a new construction of the modes of the Poincaré dodecahedral space S3=I. The construction uses the Hopf map, Maxwell's multipole vectors and orbifolds. In particular, the *235-orbifold serves as a parameter space for the modes of S3=I, shedding new light on the geometrical significance of the dimension of each space of k-modes, as well as on the modes themselves.

Mots clés: Gravitation and cosmology; Astrophysics and astroparticles

Domaines: Physique mathématique [math-ph]; Cosmologie et astrophysique extra-galactique [astro-ph.CO]; Cosmologie et astrophysique extra-galactique [astro-ph.CO]; Topologie géométrique [math.GT]

M. Lachièze-Rey, J. Weeks. Orbifold construction of the modes of the Poincaré dodecahedral space. Journal of Physics A: Mathematical and Theoretical, 2008, 41 (29), pp.295209. ⟨10.1088/1751-8113/41/29/295209⟩. ⟨hal-00218221⟩