Igor Belegradek

Igor Belegradek

Professor
School of Mathematics
Georgia Institute of Technology
office: Skiles 240B
email: ib at math dot gatech dot edu

Mailing address: School of Mathematics
Georgia Tech, 686 Cherry Street,
Atlanta, GA 30332-0160
phone: (404) 385-0053
fax: (404) 894-4409
Research Interests:
    My general research interests are in geometry, topology, and group theory. Current interests include moduli spaces of nonnegatively curved metrics, and ends of nonpositively curved manifolds.

Papers (which either come in PDF or can be found at the arXiv by clicking here )

  • 50. (with M. Ghomi) Point selections from Jordan domains in Riemannian Surfaces, https://arxiv.org/abs/2308.03697, 17 pages, to appear in Trans. Amer. Math. Soc..
  • 49. (with B. Liu) Four manifolds with no smooth spines, 11 pages, arXiv:2102.11416, 2021, to appear in Math. Res. Lett..
  • 48. Hyperbolization and regular neighborhoods, 27 pages, arXiv:2011.01320, 2020.
  • 47. (with D. Gonzalez-Alvaro) Diffeomorphic souls and disconnected moduli spaces of nonnegatively curved metrics, 12 pages, arXiv:2005.05755, 2020, to appear in Annales l'Institut Fourier.
  • 46. Iterated circle bundles and infranilmanifolds, Osaka J. Math.57 (2020), no. 1, 165–168.
  • 45. Index theory and deformations of open nonnegatively curved manifolds, 18 pages, 2018, to appear in J. Differential Geom..
  • 44. (with M. Ghomi) Centers of disks in Riemannian manifolds, Pacific J. Math. 304 (2020) No. 2, 401-418.
  • 43. Gromov-Hausdorff hyperspace of nonnegatively curved 2-spheres, Proc. Amer. Math. Soc. 146 (2018), no. 4, 1757–1764.
  • 42. Hyperspaces of smooth convex bodies up to congruence, Adv. Math. 332 (2018), 176–198.
  • 41. Higher homotopy groups of spaces of nonnegatively curved metrics , pp 19-21, Oberwolfach Report No. 03/2017, .pdf.
  • 40. Spaces of nonnegatively curved surfaces, pp 16-19, Oberwolfach Report No. 03/2017, .pdf.
  • 39. (with Z. Jiang) Smoothness of Minkowski sum and generic rotations, J. Math. Anal. Appl, 450 (2017), no. 2, 1229-1244.
  • 38. (with T. Banakh) Spaces of nonnegatively curved surfaces, J. Math. Soc. Japan, 70 (2018) 733-756.
  • 37. (with F. T. Farrell and V. Kapovitch) Space of nonnegatively curved metrics and pseudoisotopies, J. Differential Geom. 105 (2017) 345-374.
  • 36. (with J. Hu) Connectedness properties of the space of complete nonnegatively curved planes, Math. Ann., 362 (2015), no. 3-4, 1273–1286. Erratum: Math. Ann. 364 (2016), no. 1-2, 711–712.
  • 35. Topology of open nonpositively curved manifolds, Geometry, Topology and Dynamics in Negative Curvature, 32-83, London Math. Soc. Lecture Note Ser., 425, Cambridge Univ. Press, Cambridge, 2016.
  • 34. An assortment of negatively curved ends, J. Topol. Anal. (2013) 05, No. 04, pp. 439-449.
  • 33. (with T. Nguyen Phan) Non-aspherical ends and nonpositive curvature, 14 pages, Trans. Amer. Math. Soc., 368 (2016), no. 8, 5363-5376.
  • 32. Obstructions to nonpositive curvature for open manifolds, Proc. Lond. Math. Soc. (2014) 109 (3), 763-784.
  • 31. Open aspherical manifolds not covered by the Euclidean space, Proc. Amer. Math. Soc. , 143 (2015), No. 8, 3641--3643.
  • 30. The space of complete nonnegatively curved metrics on the plane, pp 18-19, Oberwolfach Report No. 01/2012, .pdf.
  • 29. (with E. Choi and N. Innami) Rays and souls in von Mangoldt planes, Pacific J. Math. 259 (2012), no 2, 279-306.
  • 28. (with C. Hruska) Hyperplane arrangements in negatively curved manifolds and relative hyperbolicity, Groups Geom. Dyn. 7 (2013), 13–38.
  • 27. (with S. Kwasik and R. Schultz) Moduli spaces of nonnegative sectional curvature and non-unique souls, J. Differential Geom. 89 (2011), no 1, 49-86. Correction: J. Differential Geom. 119 (2021), 183-185.
  • 26. (with S. Kwasik and R. Schultz) Codimension two souls and cancellation phenomena, Advances in Math. 275 (2015), 1-46.
  • 25. Complex hyperbolic hyperplane complements, Math. Annalen 353 (2012), no. 2, 545-579.
  • 24. Rigidity and Relative Hyperbolicity of Real Hyperbolic Hyperplane Complements, Pure Appl. Math. Q. 8 (2012), no. 1, 15-52, Special Issue: In honor of Farrell-Jones.
  • 23. Degenerations of Riemannian manifolds (expository note containing two articles written for Modern Encyclopedia of Mathematical Physics which it seems will not be published), accepted, 11 pages.
  • 22. (with D. Osin) Rips construction and Kazhdan property (T), Groups, Geom., Dyn. 2 (2008) no. 1, 1-12.
  • 21. (with A. Szczepanski and O. V. Belegradek) Endomorphisms of relatively hyperbolic groups, 11 pages, Internat. J. Algebra Comput. 18 (2008) no. 1, 97-110
  • 20. Aspherical manifolds with relatively hyperbolic fundamental groups, Geom. Dedicata 129 (2007) no. 1, 119-144
  • 19. Aspherical manifolds, relative hyperbolicity, simplicial volume, and assembly maps, Algebr. Geom. Topol. 6 (2006) 1341-1354.
  • 18. (with V. Kapovitch) Classification of negatively pinched manifolds with amenable fundamental groups, Acta Math. 196 (2006), no. 2 , 229-260
  • 17. (with V. Kapovitch) Pinching estimates for negatively curved manifolds with nilpotent fundamental groups, Geom. Funct. Anal. 12 (2005) no. 5, 929-938
  • 16. (with G. Wei) Metrics of positive Ricci curvature on bundles, Int. Math. Res. Not., (2004) no. 57, 3079--3096.
  • 15. Nonnegative curvature, symmetry, and fundamental group, Geom. Dedicata 106 (2004), no. 1, 169--184.
  • 14. On co-Hopfian nilpotent groups, Bull. London Math. Soc.,; 7 pp. 35 (2003), no. 6, 805--811.
  • 13. Vector bundles with infinitely many souls, Proc. Amer. Math. Soc., 131 (2003), no. 7, 2217-2221.
  • 12. Pinching surface groups in complex hyperbolic plane, 97 (2003) Geom. Dedicata, no. 1, 45-54.
  • 11. (with V. Kapovitch) Obstructions to nonnegative curvature and rational homotopy theory, J. Amer. Math. Soc., 16 (2003), no. 7, 259-284.
  • 10. (with G. Wei) Metrics of positive Ricci curvature on vector bundles over nimanifolds, Geom. Funct. Anal., 12 (2002), no. 7, 56-72.
  • 9. On Mostow Rigidity for variable negative curvature, Topology, 41 (2002), no.2, 341-361.
  • 8. (with V. Kapovitch) Finiteness theorems for nonnegatively curved vector bundles, Duke Math. J., 108 (2001), 109-134.
  • 7. (with V. Kapovitch) Topological obstructions to nonnegative curvature, Math. Ann., 320 (2001), 167-190.
  • 6. Pinching, Pontrjagin classes, and negatively curved vector bundles, Invent. Math., 144 (2001), 353-379.
  • 5. Lipschitz precompactness for closed negatively curved manifolds, Proc. Amer. Math. Soc, 127 (1999), 1201-1208, .pdf.
  • 4. Counting open negatively curved manifolds up to tangential homotopy equivalence, J. Differential Geom., 50 (1998), 59-88
  • 3. Intersections in hyperbolic manifolds, Geometry and Topology, 2 (1998), 117-144.
  • 2. Some curious Kleinian groups and hyperbolic 5-manifolds, Transformation Groups, 2 (1997), no. 1, 3-29, .pdf.
  • 1. Conformally flat Seifert manifolds, Siberian Advances in Mathematics, 3 (1993), no. 1, 1-18., .pdf.
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