email : elisha.falbel at imj-prg.fr
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M2 de Mathématiques fondamentales
Travaux récents :
Character varieties for SL(3,C): the figure eight knot. Avec A. Guilloux, P.-V. Koseleff, F. Rouillier, M. Thistlethwaite.
(arxiv ) 2014.
Duality and invariants of representations of fundamental groups of 3-manifolds into PGL(3,C). Avec Q. Wang. (arxiv ) 2014.
A flag structure on a cusped hyperbolic 3-manifold. Avec R. S. Thebaldi. ( Hal). To appear in Pacific J. Math.
Diffeomorphisms preserving R-circles in three dimensional CR manifolds. Avec J. M. Veloso.
( pdf). 2013. To appear in Math. Nachr.
Representations of fundamental groups of 3-manifolds
into PGL(3;C): Exact computations in low complexity. Avec P.-V. Koseleff et F. Rouillier.
( pdf). 2013. To appear in Geom. Dedicata.
Branched spherical CR structures on the complement of the figure eight knot. Avec Jieyan Wang.
( pdf). 2013. Michigan Math. J. 63 (2014), no. 3, 635-667.
Complex hyperbolic geometry of the figure eight knot. Avec Martin Deraux. ( pdf). Geom. Topol. 19 (2015), no. 1, 237-293.
Local rigidity for SL(3,C) representations of 3-manifolds groups. Avec N. Bergeron, A. Guilloux, P.-V. Koseleff et F. Rouillier. ( pdf) 2012. Exp. Math. 22 (2013), no. 4, 410-420.
Tetrahedra of flags, volume and homology of SL(3). Avec N. Bergeron et A. Guilloux. ( pdf). 2011. Geom. Topol. 18 (2014), no. 4, 1911-1971.
A combinatorial invariant for Spherical CR structures. Avec Qingxue Wang. ( pdf). 2010. Asian J. Math. 17 (2013), no. 3, 391-422.
A Lorentz form associated to contact sub-conformal and CR manifolds. Avec J. M. Veloso. Kodai Math. J. 37 (2014), no. 2, 405-426.
Travaux moins récents :
Generators of a Picard modular group in two complex dimensions. Avec Gábor Francsics, Peter D. Lax et John Parker.
Proc. Amer. Math. Soc. 139 (2011), no. 7, 2439-2447
The geometry of the Gauss-Picard modular group. Avec Gábor Francsics et John Parker.
Math. Ann. 349 (2011), no. 2, 459-508.
A Volume function for Spherical CR tetrahedra.
Quarterly Journal of Math. 62 (2011), no. 2, 397 - 415.
( ps)
The PU(2,1) configuration space of four points in S3 and the Cross-Ratio Variety. Avec Ioannis Platis.
Math. Annalen. 340 (2008), no. 4, 935-962.
( ps)
Compacité à la Mahler-Mumford pour les
groupes fuchsiens dans un espace symétrique de rang un. Avec Richard Wentworth. ( pdf).
New version:
On Products of Isometries of Hyperbolic Space.
Topology Appl. 156 (2009), no. 13, 2257-2263.( pdf).
Geometric structures associated to triangulations as fixed point
sets of involutions.
Topology and its Applications 154 (2007), no. 6, 1041-1052. ( pdf). New version with some corrections ( ps).
A spherical CR structure on the complement of the figure
eight knot with discrete holonomy. Yet another version.
Journal of Differential Geometry. 79 (2008), no. 1, 69-110.
( ps)
Unitary Representations and triples of Lagrangians. Avec Richard Wentworth.
Topology 45 (2006), no. 1, 65-99.
( ps)
A bilinear form associated to contact sub-conformal and
CR-manifolds. Avec Jose Miguel Veloso.
Journal of Differential
Geometry and its Applications.
( ps)
The geometry of Eisenstein-Picard modular group. Avec John Parker.
Duke Math. Journal 131 (2006), no. 2, 249--289.
( ps)
New constructions of fundamental polyhedra in complex hyperbolic space.
Avec Martin Deraux et Julien Paupert.
Acta Mathematica 194 (2005), 155-201.
( pdf)
Fundamental domains for finite subgroups of U(2) and
Configurations of Lagrangians. Avec Julien Paupert.
Geom. Dedicata 109 (2004), 221--238.
( ps)
Classifying triples of Lagrangians in a Hermitian vector space. Avec J.-P. Marco, F. Schaffhauser.
Topology Appl. 144 (2004), no. 1-3, 1--27.
( pdf)
Measures of Transverse Paths in Sub-Riemannian Geometry. Avec F. Jean.
J. Anal. Math. 91 (2003), 231--246. ( ps)
The moduli space of the modular group in complex hyperbolic geometry. Avec J. Parker.
Inventiones Mathematicae. 152 (2003), no. 1, 57--88.
(ps)
A simple proof of the Riemann Mapping Theorem for
Domains with Spherical Boundary.
Complex Var. Theory Appl. 48 (2003), no. 3, 277--282.( ps)
A circle of Modular groups in PU(2,1). Avec P.-V. Koseleff.
Math. Res. Lett. 9 (2002), no. 2-3, 379--39
( ps)
Rigidity and flexibility of triangle groups in complex hyperbolic geometry. Avec P.-V. Koseleff.
Topology 41 (2002), no. 4, 767--786
( ps)
Finite groups generated by involutions on Lagrangian planes of C^2.
Canad. Math. Bull. 44 (2001), no. 4, 408--419
( ps)