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

 Access to full text

 Full (PDF)

1. M. F. Atiyah ; Convexity and commuting Hamiltonians. Bull. London Math. Soc. 14(1) (1982), 1–15. Zbl0482.58013MR642416
2. A. Alekseev, A. Malkin, E. Meinrenken ; Lie group valued moment maps. J. Diff. Geom. 48(3) (1998), 445–495. Zbl0948.53045MR1638045
3. S. Agnihotri, C. Woodward ; Eigenvalues of products of unitary matrices and quantum Schubert calculus. Math. Res. Lett. 5(6) (1998), 817–836. Zbl1004.14013MR1671192
4. P. Belkale ; Local systems on $P^1-S$ for $S$ a finite set. Compositio Math. 129(1) (2001), 67–86. Zbl1042.14031MR1856023
5. 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. Zbl0939.14015MR1644048
6. 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. Zbl0982.14022MR1796505
7. J.H. Conway, A.J. Jones. Trigonometric diophantine equations (On vanishing sums of roots of unity). Acta Arithmetica 30 (1976), 229–240. Zbl0349.10014MR422149
8. P. Deligne, G. D. Mostow ; Monodromy of hypergeometric functions and non-lattice integral monodromy. Publ. Math. IHES 63 (1986), 5–89. Zbl0615.22008MR849651
9. M. Deraux, E. Falbel, J. Paupert ; New constructions of fundamental polyhedra in complex hyperbolic space. Acta Math. 194 (2005), 155–201. Zbl1113.22010MR2231340
10. E. Falbel, J. Paupert ; Fundamental domains for finite subgroups in $U\left(2\right)$ and configurations of Lagrangians. Geom. Dedicata 109 (2004), 221–238. Zbl1108.51018MR2114077
11. E. Falbel, R. Wentworth ; Eigenvalues of products of unitary matrices and Lagrangian involutions. Topology 45 (2006), 65–99. Zbl1081.58006MR2170495
12. E. Falbel, R. Wentworth ; Produits d’isométries d’un espace symétrique de rang un et compacité à la Mumford-Mahler. Preprint 2006. 
13. E. Falbel, V. Zocca ; A Poincaré’s polyhedron theorem for complex hyperbolic geometry. J. Reine Angew. Math. 516 (1999), 138–158. Zbl0944.53042
14. W. Fulton ; Eigenvalues, invariant factors, highest weights, and Schubert calculus. Bull. Amer. Math. Soc. 37(3) (2000), 209–249. Zbl0994.15021MR1754641
15. W.M. Goldman ; Complex Hyperbolic Geometry. Oxford Mathematical Monographs. Oxford Science Publications (1999). Zbl0939.32024MR1695450
16. V. Guillemin, S. Sternberg ; Convexity properties of the moment mapping. Invent. Math. 67(3) (1982), 491–513. Zbl0503.58017MR664117
17. V. Guillemin, S. Sternberg ; Convexity properties of the moment mapping II. Invent. Math. 77(3) (1984), 533–546. Zbl0561.58015MR759258
18. V. T. Khoi ; On the $SU(2,1)$ character variety of the Brieskorn homology spheres. Preprint. 
19. A. Klyachko ; Stable bundles, representation theory and Hermitian operators. Selecta Math. (NS) 4(3) (1998), 419–445. Zbl0915.14010MR1654578
20. 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). Zbl1062.14054MR1957068
21. V. P. Kostov ; The Deligne-Simpson problem–a survey. J. Algebra 281 (2004), 83–108. Zbl1066.15016MR2091962
22. G. D. Mostow ; On a remarkable class of polyhedra in complex hyperbolic space. Pacific J. Math. 86 (1980), 171–276. Zbl0456.22012MR586876
23. G. D. Mostow ; Generalized Picard lattices arising from half-integral conditions. Publ. Math. IHES 63 (1986), 91–106. Zbl0615.22009MR849652
24. J. R. Parker ; Unfaithful complex hyperbolic triangle groups. Prépublication (2005). 
25. J. R. Parker, J. Paupert ; Unfaithful complex hyperbolic triangle groups II : Higher order reflections. En préparation. 
26. 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/ 
27. J. Paupert ; Elliptic triangle groups in $PU(2,1)$, Lagrangian triples and momentum maps. Preprint (2006). A paraître dans Topology. Zbl1131.22010MR2313070
28. J.K. Sauter ; Isomorphisms among monodromy groups and applications to lattices in $PU(1,2)$. Pacific J.Maths. 146 (1990), 331–384. Zbl0759.22013MR1078386
29. F. Schaffhauser ; Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups. Thèse de doctorat de l’Université Paris 6, 2005. 
30. 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. Zbl1022.53034MR1957045
31. W. P. Thurston ; Shapes of polyhedra and triangulations of the sphere. Geometry and Topology Monographs 1, the Epstein Birthday Schrift (1998), 511–549. Zbl0931.57010MR1668340
32. A. Weinstein ; Poisson geometry of discrete series orbits, and momentum convexity for noncompact group actions. Lett. Math. Phys. 56(1) (2001), 17-30. Zbl1010.53060MR1848163
33. P. Will ; Groupes libres, groupes triangulaires et tore épointé dans $PU(2,1)$. Thèse de doctorat de l’Université Paris 6 (2006).