Nansen Petrosyan


Ph.D. University of Wisconsin-Madison
Professor
Department of Mathematics
University of Southampton
n dot last name at soton dot ac dot uk
B.S. Department of Mathematics, Brigham Young University, 1997-2000

Ph.D. Department of Mathematics, University of Wisconsin-Madison, 2001-2006

Visiting Assistant Professor, Department of Mathematics, Indiana Univesity, 2006-07

Postdoctoral Fellow, Department of Mathematics, KU Leuven, 2007-2013

Visiting Positions: University of British Columbia, Canada (Winter 2005), University of Neuchatel, Switzerland (May 2009),

Max Planck Institute, Bonn, Germany (May 2010, March 2012), University of Gdansk, Poland (April 2013, November 2015)


Research Interests

General Areas
Geometric Group Theory and its connections to Geometry and Topology

Specific Interests
  • Geometric, cohomological and analytic properties of groups
  • Group theoretic Dehn fillings
  • L2-Betti numbers of groups
  • Splittings of groups over codimension-one subgroups
  • Crystallographic groups and their relatives
  • Flat and almost-flat manifolds

Publications

  1. Simple groups with strong fixed-point properties,
    (2025), preprint.

  2. L2-Betti numbers of Dehn fillings, (joint with B. Sun)
    (2024), preprint.

  3. Cohomological characterisation of hyperbolicity, (joint with F. Milizia, A. Sisto, an V. Vankov)
    (2024), preprint.

  4. Asymptotic mapping class groups of Cantor manifolds and their finiteness properties, (joint with J. Aramayona, K.-U. Bux, J. Flechsig, X. Wu, appendix by O. Randal-Williams)
    Revista Matemática Iberoamericana (2024), available online.

  5. Hyperbolicity and bounded-valued cohomology, (joint with V. Vankov)
    Mathematische Annalen 390 (2024), 4701 - 4727.

  6. Cohomology of group theoretic Dehn fillings II, (joint with B. Sun)
    Advances in Mathematics 437 (2024), paper no. 109412, 56 pp.

  7. Cohomological and geometric invariants of simple complexes of groups, (joint with T. Prytula)
    Algebraic & Geometric Topology 24 (2024), no. 2, 1121 - 1155.

  8. Fibering flat manifolds of diagonal type and their fundamental groups, (joint with H. Y. Chung)
    International Journal of Algebra and Computation 32 (2022), no. 7, 1411 - 1445.

  9. Decomposing groups by codimension-1 subgroups,
    Proceedings of the American Mathematical Society 150 (2022), no. 7, 4587 - 4601.

  10. Bestvina complex for group actions with a strict fundamental domain, (joint with T. Prytula)
    Groups, Geometry, and Dynamics 14 (2020), no. 4, 1277 - 1307.

  11. Spin structures of flat manifolds of diagonal type, (joint with R. Lutowski, J. Popko, and A. Szczepanski)
    Homology, Homotopy and Applications 21 (2019), no. 2, 333 - 444.

  12. Hierarchically cocompact classifying spaces for mapping class groups of surfaces, (joint with B. E. A. Nucinkis)
    Bulletin of the London Mathematical Society 50 (2018), 569 - 582.

  13. Classification of spin structures on four-dimensional almost-flat manifolds, (joint with R. Lutowski and A. Szczepanski)
    Mathematika 64 (2018), 253-266.

  14. On dimensions of groups with cocompact classifying spaces for proper actions, (joint with I. J. Leary)
    Advances in Mathematics 311 (2017), 730 - 747.

  15. Complete Bredon cohomology and its applications to hierarchically defined groups, (joint with B. E. A. Nucinkis)
    Mathematical Proceedings of the Cambridge Philosophical Society 161 (2016), no. 1, 143 - 156.

  16. Spin structures on almost-flat manifolds, (joint with A. Gasior and A. Szczepanski)
    Algebraic & Geometric Topology 16 (2016), no. 2, 783 - 796.

  17. Bredon cohomological dimensions for groups acting on CAT(0)-spaces, (joint with D. Degrijse)
    Groups, Geometry, and Dynamics 9 (2015), no. 4, 1231-1265.

  18. Classifying spaces with virtually cyclic stabilizers for linear groups, (joint with D. Degrijse and R. Koehl)
    Transformation Groups 20 (2015) no. 2, 381 - 394.

  19. Action-induced nested classes of groups and jump cohomology,
    Forum Mathematicum 27 (2015), no. 3, 1591-1612.

  20. Crystallographic actions on contractible algebraic manifolds, (joint with K. Dekimpe)
    Transactions of the American Mathematical Society (2015) 367 (4), 2765-2786.

  21. Geometric dimension of groups for the family of virtually cyclic subgroups, (joint with D. Degrijse)
    Journal of Topology (2014) 7 (3), 697-726.

  22. F-structures and Bredon-Galois cohomology, (joint with D. Degrijse)
    Applied Categorical Structures 21 (2013), 545-586.

  23. Commensurators and classifying spaces with virtually cyclic stabilizers, (joint with D. Degrijse)
    Groups, Geometry, and Dynamics 7 (2013), no. 3, 543-555.

  24. On cohomology of crystallographic groups with cyclic holonomy of split type, (joint with B. Putrycz)
    Journal of Algebra 367 (1) (2012), 237-246

  25. On generators of crystallographic groups and actions on flat orbifolds, (joint with A. Adem, K. Dekimpe, and B. Putrycz)
    Journal of Group Theory 15 (2012), 553-561

  26. Intermediaries in Bredon (co)homology and classifying spaces, (joint with F. Dembegioti and O. Talelli)
    Publicacions Matemàtiques 56 (2) (2012), 393-412

  27. On cohomology of split Lie algebra extensions, (joint with D. Degrijse)
    Journal of Lie Theory 22 (1) (2012), 1-15

  28. Characteristic classes for cohomology of split Hopf algebra extensions, (joint with D. Degrijse)
    Journal of Algebra 332 (2011), 366-385

  29. Fiberwise volume non-increasing diffeomorphisms on product manifolds, (joint with D. Dreesen), (extended version)
    Geometriae Dedicate 149 (2010), 417-424

  30. Homology of Hantzsche-Wendt groups, (joint with K. Dekimpe)
    Contemporary Mathematics AMS 501 (2009), 87-103

  31. Cohomology of split group extensions and characteristic classes,
     Journal of Algebra 321 (2009), 2916-2925

  32. Compatible actions and cohomology of crystallographic groups, (joint with A. Adem, J. Ge, and J. Pan),
    Journal of Algebra 320 (2008), 341-353

  33. Jumps in cohomology and free group actions,
     Journal of Pure and Applied Algebra 210 (2007), 695-703

  34. Jumps in cohomology of groups,
    Mathematics in Higher School 2(1) (2006), 11-15. Ministry of Education and Sciences of Republic of Armenia.

  35. Classification of singular fibres of rational elliptic surfaces in characteristic three, (joint with T. Jarvis, W. Lang, G. Rimmasch, J. Roger, and E. Summers),
    Communications in Algebra 33 (2005), 1-34


Notes

  • Types of manifolds and Poincaré complexes, (joint with J. F. Davis)
    Survey notes.


    • Students and Postdocs

  • Vladimir Vankov EPSRC Postdoctoral Fellow 2021-22

  • Tomasz Prytula EPSRC Postdoctoral Fellow 2017-18

  • Kevin Li, PhD 2022
    Thesis subject: Bounded cohomology of groups

  • Ho Yiu Chung PhD 2020
    Thesis subject: Bieberbach groups and fibering flat manifolds of diagonal type

  • Ana Lopes Onorio PhD 2018
    Thesis subject: Relative ends of groups and Bredon cohomology
    joint with Ian Leary

  • Dieter Degrijse PhD 2013
    Thesis subject: Cohomology of split extensions and classifying spaces for families of subgroups

  • Jeroen Wynen MS 2013
    Thesis subject: The construction of buildings and the correspondence with groups

    • Current Teaching

    Hyperbolic Geometry - MATH 6079 Semester I (University of Southampton)