arXiv subjects

Elisha Falbel

Publications and source records attributed to Elisha Falbel.

21 records · Page 2Linked to original sources

arXiv2009

A Volume Function for CR Tetrahedra

We define a volume function on configurations of four points in the 3-sphere which is invariant under the action of PU(2,1), the automorphism group of the CR structure defined on the sphere by its embedding in complex 2-space. We show that the volume function, constructed using appropriate combinations of the dilogathm function of Bloch-Wigner, satisfies a five term relation in a more general context which includes at the same time CR and real hyperbolic geometry.

math.MG↗

arXiv2005

Eigenvalues of Products of Unitary Matrices and Lagrangian Involutions

This paper introduces a submanifold of the moduli space of unitary representations of the fundamental group of a punctured sphere with fixed local monodromy. The submanifold is defined via products of involutions through Lagrangian subspaces. We show that the moduli space of Lagrangian representations is a Lagrangian submanifold of the moduli of unitary representations.

math.GT↗

arXiv2005

A spherical CR structure on the complement of the figure eight knot with discrete holonomy

We describe a general geometrical construction of spherical CR structures. We construct then spherical CR structures on the complement of the figure eight knot and the Whitehead link. They have discrete holonomies contained in $PU(2,1,{\bf Z}[ω])$ and $PU(2,1,{\bf Z}[i])$ respectively. These are the same ring of integers appearing in the real hyperbolic geometry of the corresponding links.

math.DG↗