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


  • PhD students: Jing Hu (Georgia Tech) and Eric Choi (Emory, defended Fall 2012; his thesis)
  • Summer 2010: REU with Melanie Stam.
  • Summer 2008: REU with Cindy Phillips; her report.

  • Research Interests:


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

    • 36. (with Jing Hu) Connectedness properties of the space of complete nonnegatively curved planes, 16 pages, to appear in Math. Ann..
    • 35. Topology of open nonpositively curved manifolds, 50 pages, to appear in the proceedings of the ICM satellite conference (Bangalore, 2010) Geometry, Topology and Dynamics in Negative Curvature, London Math Society Lecture Notes series.
    • 34. An assortment of negatively curved ends, 11 pages. to appear in J. Topol. Anal..
    • 33. (with T. Nguyen Phan) Non-aspherical ends and nonpositive curvature, 16 pages, to appear in Trans. Amer. Math. Soc..
    • 32. Obstructions to nonpositive curvature for open manifolds, 27 pages, to appear in Proc. Lond. Math. Soc..
    • 31. Open aspherical manifolds not covered by the Euclidean space, 3 pages. to appear in Proc. Amer. Math. Soc..
    • 30. The space of complete nonnegatively curved metrics on the plane, pp 18-19, Obewolfach Report No. 01/2012, .pdf.
    • 29. (with E. Choi and N. Innami) Rays and souls in von Mongoldt 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.
    • 26. (with S. Kwasik and R. Schultz) Codimension two souls and cancellation phenomena, 34 pages, 2009.
    • 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), 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 Oleg. 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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