Applications moment, polygones de configurations et groupes discrets de réflexions complexes dans $PU(2,1)$

Paupert, Julien

Séminaire de théorie spectrale et géométrie, Tome 24 (2005-2006), pp. 45-60.

[A] M. F. Atiyah ; Convexity and commuting Hamiltonians. Bull. London Math. Soc. 14(1) (1982), 1–15. | MR | Zbl

[AMM] A. Alekseev, A. Malkin, E. Meinrenken ; Lie group valued moment maps. J. Diff. Geom. 48(3) (1998), 445–495. | MR | Zbl

[AW] S. Agnihotri, C. Woodward ; Eigenvalues of products of unitary matrices and quantum Schubert calculus. Math. Res. Lett. 5(6) (1998), 817–836. | MR | Zbl

[Be] P. Belkale ; Local systems on $P^1-S$ for $S$ a finite set. Compositio Math. 129(1) (2001), 67–86. | MR | Zbl

[Bi1] I. Biswas ; A criterion for the existence of a parabolic stable bundle of rank two over the projective line. Internat. J. Math. 9(5) (1998), 523–533. | MR | Zbl

[Bi2] I. Biswas ; On the existence of unitary flat connections over the punctured sphere with given local monodromy around the punctures. Asian J. Math. 3(2) (1999), 333–344. | MR | Zbl

[CJ] J.H. Conway, A.J. Jones. Trigonometric diophantine equations (On vanishing sums of roots of unity). Acta Arithmetica 30 (1976), 229–240. | MR | Zbl

[DM] P. Deligne, G. D. Mostow ; Monodromy of hypergeometric functions and non-lattice integral monodromy. Publ. Math. IHES 63 (1986), 5–89. | Numdam | MR | Zbl

[DFP] M. Deraux, E. Falbel, J. Paupert ; New constructions of fundamental polyhedra in complex hyperbolic space. Acta Math. 194 (2005), 155–201. | MR | Zbl

[FPau] E. Falbel, J. Paupert ; Fundamental domains for finite subgroups in $U\left(2\right)$ and configurations of Lagrangians. Geom. Dedicata 109 (2004), 221–238. | MR | Zbl

[FW1] E. Falbel, R. Wentworth ; Eigenvalues of products of unitary matrices and Lagrangian involutions. Topology 45 (2006), 65–99. | MR | Zbl

[FW2] E. Falbel, R. Wentworth ; Produits d’isométries d’un espace symétrique de rang un et compacité à la Mumford-Mahler. Preprint 2006.

[FZ] E. Falbel, V. Zocca ; A Poincaré’s polyhedron theorem for complex hyperbolic geometry. J. Reine Angew. Math. 516 (1999), 138–158. | Zbl

[F] W. Fulton ; Eigenvalues, invariant factors, highest weights, and Schubert calculus. Bull. Amer. Math. Soc. 37(3) (2000), 209–249. | MR | Zbl

[G] W.M. Goldman ; Complex Hyperbolic Geometry. Oxford Mathematical Monographs. Oxford Science Publications (1999). | MR | Zbl

[GS1] V. Guillemin, S. Sternberg ; Convexity properties of the moment mapping. Invent. Math. 67(3) (1982), 491–513. | MR | Zbl

[GS2] V. Guillemin, S. Sternberg ; Convexity properties of the moment mapping II. Invent. Math. 77(3) (1984), 533–546. | MR | Zbl

[Kh] V. T. Khoi ; On the $SU(2,1)$ character variety of the Brieskorn homology spheres. Preprint.

[Kl1] A. Klyachko ; Stable bundles, representation theory and Hermitian operators. Selecta Math. (NS) 4(3) (1998), 419–445. | MR | Zbl

[Kl2] A. Klyachko ; Vector bundles, linear representations, and spectral problems. Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002), 599–613, Higher Ed. Press, Beijing (2002). | MR | Zbl

[Ko] V. P. Kostov ; The Deligne-Simpson problem–a survey. J. Algebra 281 (2004), 83–108. | MR | Zbl

[Mos1] G. D. Mostow ; On a remarkable class of polyhedra in complex hyperbolic space. Pacific J. Math. 86 (1980), 171–276. | MR | Zbl

[Mos2] G. D. Mostow ; Generalized Picard lattices arising from half-integral conditions. Publ. Math. IHES 63 (1986), 91–106. | Numdam | MR | Zbl

[Par] J. R. Parker ; Unfaithful complex hyperbolic triangle groups. Prépublication (2005).

[ParPau] J. R. Parker, J. Paupert ; Unfaithful complex hyperbolic triangle groups II : Higher order reflections. En préparation.

[Pau1] J. Paupert ; Configurations de lagrangiens, domaines fondamentaux et sous-groupes discrets de $PU(2,1)$. Thèse de doctorat de l’Université Paris 6 (2005). http://www.institut.math.jussieu.fr/theses/2005/paupert/

[Pau2] J. Paupert ; Elliptic triangle groups in $PU(2,1)$, Lagrangian triples and momentum maps. Preprint (2006). A paraître dans Topology. | MR | Zbl

[Sa] J.K. Sauter ; Isomorphisms among monodromy groups and applications to lattices in $PU(1,2)$. Pacific J.Maths. 146 (1990), 331–384. | MR | Zbl

[Sf] F. Schaffhauser ; Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups. Thèse de doctorat de l’Université Paris 6, 2005.

[Sz] R. E. Schwartz ; Complex hyperbolic triangle groups. Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002), 339–349, Higher Ed. Press, Beijing, 2002. | MR | Zbl

[Th] W. P. Thurston ; Shapes of polyhedra and triangulations of the sphere. Geometry and Topology Monographs 1, the Epstein Birthday Schrift (1998), 511–549. | MR | Zbl

[We] A. Weinstein ; Poisson geometry of discrete series orbits, and momentum convexity for noncompact group actions. Lett. Math. Phys. 56(1) (2001), 17-30. | MR | Zbl

[Wi] P. Will ; Groupes libres, groupes triangulaires et tore épointé dans $PU(2,1)$. Thèse de doctorat de l’Université Paris 6 (2006).