List of my papers

Sometimes you get the bear, sometimes the bear gets you!


Published:

1. (with N. Gusevskii), Conformal structures on 3- manifolds, Soviet Math. Dokl., Vol. 34 (1987) p. 314-318.

2. Some properties of developing maps of conformal structures on 3-manifolds, Soviet Math. Dokl., Vol. 35 (1987) p. 146-149.

3. On conformal structures with Fuchsian holonomy, Soviet Math. Dokl., Vol. 38 (1989) N 1, p. 14-17.

4. Kleinian Groups and Flat Conformal Structures, Ph. D. thesis, Institute of Mathematics, Siberian Branch of Soviet Academy of Sci., Novosibirsk (1988).

5. Deformation spaces of flat conformal structures, In: "Proceedings of the Second Soviet-Japan Joint Symposium on Topology" (Khabarovsk, 1989), Answers and Questions in General Topology, Vol. 8 (1990) N 1, p. 253-264.

6. (with L. Potyagailo), On absence of Ahlfors' and Sullivan's finiteness theorems for Kleinian groups in higher dimensions, Siberian Math. Journ., Vol. 32 (1991)  N 2, p. 61-73.

7. (with L. Potyagailo), On absence of Ahlfors' finiteness theorem for Kleinian groups in dimension 3, Topology and its Applications, Vol. 40 (1991) p. 83-91.

8. Deformations of representations of fundamental groups of 3-manifolds, Siberian Math. Journ., Vol. 32 (1991), N 1, p. 43-49.

9. Flat conformal structures on 3-manifolds. The existence problem: I, Siberian Math. Journ., Vol. 30 (1989), N 5, p. 60-73.

10. Flat conformal structures on 3-manifolds (survey), In: "Proceedings of International Conference dedicated to A. Maltsev", Novosibirsk, 1989. Contemporary Mathematics, 1992, Vol. 131.1, p. 551-570.

11. On absence of Sullivan's cusp finiteness theorem in higher dimensions. In: "Algebra and analysis" (Irkutsk, 1989), p. 77-89. Amer. Math. Soc. Transl. Ser. 2, Vol. 163, Amer. Math. Soc., Providence, RI, 1995.

12. Flat conformal structures on 3-manifolds, I-- III, Journal of Diff. Geometry (Part I appeared in Vol. 38, N 1, 1993).

13. Deformations of representations of discrete subgroups of SO(3,1), Math. Annalen, Vol. 299 (1994) p. 341-354.

14. On monodromy of complex projective structures, Inventiones Math., Vol. 119 (1995) p. 243-265.

15. (with J. Millson), On the moduli spaces of polygons in the Euclidean plane, Journal of Diff. Geometry, Vol. 42 (1995) N 1, p. 133-164.

16. (with B. Leeb), On asymptotic cones and quasi-isometry classes of fundamental groups of nonpositively curved manifolds, Geometric Analysis and Functional Analysis, Vol. 5 (1995) N 3, p. 582-603.

17. (with J. Millson), The relative deformation theory of flat connections and deformations of linkages in spaces of constant curvature, Compositio Math., Vol. 103 (1996)  N 3, p. 287-317.

18. (with J. Millson), On the deformation theory of representations of fundamental groups of hyperbolic 3-manifolds, Topology, Vol. 35, N 4 (1996) p. 1085-1106.

19. (with J. Millson), The symplectic geometry of polygons in Euclidean space, Journal of Diff. Geometry, Vol. 44 (1996) p. 479-513.

20. (with B. Leeb), Actions of discrete groups on Hadamard spaces, Math. Annalen, Bd. 306 (1996) p. 341-352.

21. (with B. Leeb), Quasi-isometries preserve the geometric decomposition of Haken manifolds, Inventiones Math., Vol. 128, F. 2 (1997) p. 393-416.

22. (with J. Millson), Hodge theory and the art of paper folding, Publications of RIMS (Kyoto), Vol. 33, (1997) N 1, p. 1-33.

23. (with B. Leeb), 3-manifold groups and nonpositive curvature, Geometric Analysis and Functional Analysis, vol. 8 (1998), N 5, p. 841-852.

24. (with B. Kleiner and B. Leeb), On quasi-isometry invariance of de Rham decomposition of nonpositively curved Riemannian manifolds, Topology, vol. 37 (1998) N 6, p. 1193-1212.

25. On dynamics of pseudo-Anosov homeomorphisms on representation varieties of surface groups, Ann. Acad. Sci. Fenn., Vol. 23 (1998) p. 83-100.

26. (with J. Millson), On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties,
Math. Publications of IHES, Vol. 88 (1999) p. 5-95.

27. (with J. Millson), Moduli spaces of linkages and arrangements, In: ``Advances in Geometry'', J.-L. Brylinski, et al (eds.), Progress in Mathematics, Birkhauser, Vol. 172 (1999) p. 237-270.

28. (with J. Millson), On the moduli space of a spherical polygonal linkage,  Canad. Math. Bull., Vol. 42 (1999) p. 307-320.

29. (with D. Gallo and A. Marden), On monodromy of Schwarzian differential equation on Riemann surfaces, Annals of Math., Vol. 151 (2000), N 2, p. 625-704.

30. (with J. Millson and T. Treloar), The symplectic geometry of polygons in hyperbolic 3-space. Asian Journal of Math., Vol. 4 (2000), N1 (Kodaira's 75-th birthday volume), p. 123-164.

31. Hyperbolic Manifolds and Discrete Groups: Lectures on Thurston's Hyperbolization, Birkhauser's series ``Progress in Mathematics'', 2000.

32. (with B. Kleiner), Hyperbolic groups with low-dimensional boundary, Ann. Sci. de ENS Paris, t. 33 (2000) p. 647-669.

33. (with W. Goldman and B. Leeb), Complex hyperbolic surfaces homotopy-equivalent to a Riemann surface, Comm. in Analysis and Geom., Vol. 9, N 1 (2001), 61-96.

34. (with J. Millson), Quantization of bending deformations of polygons in E3 , hypergeometric integrals and the Gassner representation, Canad. Math. Bull., Vol. 44 (2001), p. 36--60.

35. (with J. Millson), Universality theorem for configuration spaces of planar linkages, Topology, Vol. 41 (2002), no. 6,  p. 1051--1107.

36.  (with M.Bestvina and B. Kleiner), Van Kampen's embedding obstruction for discrete groups,  Inventiones Math.,  Vol. 150 (2002) no. 2,  p. 219-235.

37. Conformally flat metrics on 4-manifolds, Journal of Diff. Geometry, Vol. 66 (2004) p. 1-13.

38. (with B. Kleiner), Coarse Alexander duality and duality groups, Journal of Differential Geometry,  Vol. 69, (2005)  Number 2, p. 279-352.

39. Flats in 3-manifolds, Annales de la Faculte des Sciences de Toulouse, Vol. 14 (2005),  F. 3, p. 459-499.

40. Representations of polygons of finite groups, Geometry and Topology, Vol. 9 (2005) Paper no. 43, p. 1915-1951.

41. Generalized triangle inequalities and their applications,  Proceedings of the International Congress of Mathematicians - Madrid, August 22-30, 2006.  Eds. Marta Sanz-Sola, Javier Soria, Juan L. Varona, Joan Verdera. Vol. 2, p. 719-742.

42. (with J. Millson),  Structure of the tensor product semigroup, Asian Math Journal (S.S.Chern memorial issue) Vol. 10, N. 3 (2006) p. 493-540.

43.  (with T. Haines and J. Millson), Appendix A to Equidimensionality of convolution morphisms and applications to saturation problems (by T. Haines),
Advances in Mathematics, Vol. 207, (2006) Issue 1, p.  321-327.

44. (with B. Kleiner), Weak hyperbolization conjecture for 3-dimensional  CAT(0) groups,  Geometry, Groups and Dynamics, Vol. 1 (2007),  p. 67-79. 

45. Triangle inequalities in path metric spaces. Geometry and Topology, Vol. 11 (2007) p. 1653-1680.

46. Verallgemeinerte Dreiecksungleichungen (Generalized Triangle Inequalities), Jahrbuch von der  Max-Planck-Gesellschaft, 2007, p. 355-358.

47. Kleinian groups in higher dimensions. In "Geometry and Dynamics of Groups and Spaces. In memory of Alexander Reznikov'', M.Kapranov et al (eds). Birkhauser, Progress in Mathematics, Vol. 265, 2007, p. 485-562.

48. Convex projective structures on Gromov-Thurston manifolds. Geometry and Topology, Vol. 11 (2007) p. 1777-1830.

49. (with L. Potyagailo and E. Vinberg), Non-coherence of some non-uniform lattices in Isom(Hn ). Geometry and Topology Monographs (Zieschang's memorial volume), Vol. 14, 2008, p. 335-351.

50. (with B. Leeb and J. Millson), The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra, Memoirs of AMS, Vol. 192, 2008.

51. (with J. Millson), A path model for geodesics in Euclidean buildings and its applications  to representation theory. Preprint, 2004. To appear in GGD.

52. (with S. Kumar and J. Millson), Saturation and irredundancy for Spin(8). Preprint, 2006. To appear in  Pure and Applied Mathematics Quarterly (Hirzebruch Special Issue).

53. Homological dimension and critical exponent of Kleinian groups. Preprint, 2007. To appear in GAFA.



Preprints and (to be) under revision or/and (to be) submitted:

1. Intersection pairing on hyperbolic 4-manifolds, Preprint of MSRI, 1992.

2. Hyperbolic 4-manifolds fibered over surfaces. Preprint, 1993.

3. Eisenstein series and Dehn surgery. Preprint of MSRI, 1992.

4.  An example of a 2-dimensional hyperbolic group which cannot act on 2-dimensional complexes of negative curvature. Preprint 1994.

5. Lecture notes on geometric group theory. University of Utah Lecture Notes, Revision: 2006. 

6. Discrete Groups and Riemann Surfaces: Notes on Teichmuller theory. University of Utah Lecture Notes, 1993.

7. On normal subgroups in the fundamental groups of complex surfaces. Preprint, 1998.

8. Periods of abelian differentials and dynamics. Preprint, 2000.

9. (with B. Leeb and J. Millson), Polygons in buildings and their refined side lengths. Preprint, 2004. Submitted to JDG.

10. (with B. Leeb and J. Millson), Convex functions on symmetric spaces, side lengths of polygons and the stability inequalities for weights configurations at infinity.
Preprint, 2004. Submitted to JDG.

11. (with B. Kleiner), Geometry of Gromov-hyperbolic spaces satisfying coarse Poincare duality. Preprint, 2004.

12. (with B. Kleiner), Geometry of quasi-planes. Preprint, 2004.

13. (with B. Kleiner), Coarse fibrations and a generalization of the Seifert fibered space conjecture. Preprint, 2004.

14. Energy of harmonic functions and Gromov's proof of Stallings' theorem,  Preprint, 2007.

15. On sequences of finitely generated discrete groups, Preprint, 2007.

16. (with B. Kleiner), Appendix to "Lacunary hyperbolic groups", by A. Olshanskii, D.Osin, M.Sapir, Preprint, 2007. Submitted.