Publications of Hansjörg Geiges


Books:
  1. An Introduction to Contact Topology,
    Cambridge Studies in Advanced Mathematics 109,
    Cambridge University Press (2008).
    Errata

  2. The Geometry of Celestial Mechanics,
    London Mathematical Society Student Texts 83,
    Cambridge University Press (2016).
    Rezension durch die Mathematical Association of America

  3. (with K. Zehmisch) A Course on Holomorphic Discs,
    Basler Lehrbücher,
    Birkhäuser Verlag (2023).

Refereed articles:
  1. Contact structures on 1-connected 5-manifolds,
    Mathematika 38 (1991), 303-311.

  2. Symplectic structures on T2-bundles over T2,
    Duke Math. J. 67 (1992), 539-555.

  3. Contact structures on (n-1)-connected (2n+1)-manifolds,
    Pacific J. Math. 161 (1993), 129-137.

  4. Symplectic manifolds with disconnected boundary of contact type,
    Int. Math. Res. Not. IMRN (1994), no. 1, 23-30.

  5. (with C. B. Thomas) Hypercontact manifolds,
    J. London Math. Soc. (2) 51 (1995), 342-352.

  6. Examples of symplectic 4-manifolds with disconnected boundary of contact type,
    Bull. London Math. Soc. 27 (1995), 278-280.

  7. (with J. Gonzalo) Contact geometry and complex surfaces,
    Invent. Math. 121 (1995), 147-209.

  8. (with J. Gonzalo) Seifert invariants of left-quotients of 3-dimensional simple Lie groups,
    Topology Appl. 66 (1995), 117-127.

  9. (with J. Gonzalo) An application of convex integration to contact geometry,
    Trans. Amer. Math. Soc. 348 (1996), 2139-2149.

  10. Symplectic couples on 4-manifolds,
    Duke Math. J. 85 (1996), 701-711.

  11. Constructions of contact manifolds,
    Math. Proc. Cambridge Philos. Soc. 121 (1997), 455-464.

  12. Normal contact structures on 3-manifolds,
    Tôhoku Math. J. 49 (1997), 415-422.

  13. (with J. Gonzalo) Contact circles on 3-manifolds,
    J. Differential Geom. 46 (1997), 236-286.

  14. Mannigfaltige Geometrien,
    Elem. Math. 52 (1997), 93-107.

  15. Applications of contact surgery,
    Topology 36 (1997), 1193-1220.

  16. (with C. B. Thomas) Contact topology and the structure of 5-manifolds with fundamental group Z2,
    Ann. Inst. Fourier (Grenoble) 48 (1998), 1167-1188.

  17. (with C. B. Thomas) Almost linear actions by finite groups on S2n-1,
    in: Proceedings of the Kirbyfest (J. Hass, M. Scharlemann, eds.),
    Geom. Topol. Monogr. 2 (1999), 135-156.

  18. (with D. Rattaggi) Periodic automorphisms of surfaces: Invariant circles and maximal orders,
    Experiment. Math. 9 (2000), 75-84.

  19. (with S. Müller) Almost complex structures on 8-manifolds,
    Enseign. Math. (2) 46 (2000), 95-107.

  20. Facets of the cultural history of mathematics,
    European Review 8 (2000), 487-497.

  21. (with C. B. Thomas) Finite group actions on the 7-sphere,
    Enseign. Math. (2) 46 (2000), 403-410.

  22. Chern numbers of almost complex manifolds,
    Proc. Amer. Math. Soc. 129 (2001), 3749-3752.

  23. A brief history of contact geometry and topology,
    Expo. Math. 19 (2001), 25-53;
    Chinese translation in Shuxue Yilin 25 (2006), 133-148.

  24. (with C. B. Thomas) Contact structures, equivariant spin bordism, and periodic fundamental groups,
    Math. Ann. 320 (2001), 685-708.

  25. (with F. Ding) Symplectic fillability of tight contact structures on torus bundles,
    Algebr. Geom. Topol. 1 (2001), 153-172.

  26. Beweis des Satzes von Morley nach A. Connes,
    Elem. Math. 56 (2001), 137-142.

  27. (with J. Gonzalo) Moduli of contact circles,
    J. Reine Angew. Math. 551 (2002), 41-85.

  28. h-Principles and Flexibility in Geometry,
    Mem. Amer. Math. Soc. 164 (2003), no. 779.

  29. (with F. Ding) A Legendrian surgery presentation of contact 3-manifolds,
    Math. Proc. Cambridge Philos. Soc. 136 (2004), 583-598.

  30. (with J. Gonzalo) On the topology of the space of contact structures on torus bundles,
    Bull. London Math. Soc. 36 (2004), 640-646.

  31. (with F. Ding and A. I. Stipsicz) Surgery diagrams for contact 3-manifolds,
    Turkish J. Math. 28 (2004), 41-74 (Proceedings of the 10th Gökova Geometry-Topology conference, 2003).

  32. (with F. Ding) E8-plumbings and exotic contact structures on spheres,
    Int. Math. Res. Not. IMRN (2004), no. 71, 3825-3837.

  33. (with F. Ding and A. I. Stipsicz) Lutz twist and contact surgery,
    Asian J. Math. 9 (2005), 57-64.

  34. Christiaan Huygens and contact geometry,
    Nieuw Arch. Wiskd. (5) 6 (2005), 117-123;
    reprinted in Newsletter European Math. Soc. 65 (September 2007), 13-19.

  35. Contact Dehn surgery, symplectic fillings, and Property P for knots,
    Expo. Math. 24 (2006), 273-280.

  36. (with F. Ding) Legendrian knots and links classified by classical invariants,
    Commun. Contemp. Math. 9 (2007), 135-162.

  37. (with F. Pasquotto) A formula for the Chern classes of symplectic blow-ups,
    J. London Math. Soc. (2) 76 (2007), 313-330.

  38. (with F. Ding) A unique decomposition theorem for tight contact 3-manifolds,
    Enseign. Math. (2) 53 (2007), 333-345.

  39. Horizontal loops in Engel space,
    Math. Ann. 342 (2008), 291-296.

  40. A contact geometric proof of the Whitney-Graustein theorem,
    Enseign. Math. (2) 55 (2009), 93-102.

  41. (with J. Gonzalo) Contact spheres and hyperkähler geometry,
    Comm. Math. Phys. 287 (2009), 719-748.

  42. (with F. Ding) Handle moves in contact surgery diagrams,
    J. Topol. 2 (2009), 105-122.

  43. (with A. I. Stipsicz) Contact structures on product five-manifolds and fibre sums along circles,
    Math. Ann. 348 (2010), 195-210.

  44. (with F. Ding) The diffeotopy group of S1× S2 via contact topology,
    Compos. Math. 146 (2010), 1096-1112.

  45. (with F. Ding) Legendrian helix and cable links,
    Commun. Contemp. Math. 12 (2010), 487-500.

  46. (with J. Gonzalo) A homogeneous Gibbons-Hawking ansatz and Blaschke products,
    Adv. Math. 225 (2010), 2598-2615.

  47. (with K. Zehmisch) Eliashberg's proof of Cerf's theorem,
    J. Topol. Anal. 2 (2010), 543-579.

  48. (with F. Ding) Neighbourhoods and isotopies of knots in contact 3-manifolds,
    Arch. Math. (Basel) 97 (2011), 391-397.

  49. Contact structures and geometric topology,
    in: Global Differential Geometry, Springer Proc. Math. 17,
    Springer-Verlag, Berlin (2012), 463-489.

  50. (with J. Gonzalo) Generalised spin structures on 2-dimensional orbifolds,
    Osaka J. Math. 49 (2012), 449-470.

  51. (with K. Zehmisch) Symplectic cobordisms and the strong Weinstein conjecture,
    Math. Proc. Cambridge Philos. Soc. 153 (2012), 261-279.

  52. (with F. Ding and O. van Koert) Diagrams for contact 5-manifolds,
    J. London Math. Soc. (2) 86 (2012), 657-682.

  53. (with F. Ding) Contact structures on principal circle bundles,
    Bull. London Math. Soc. 44 (2012), 1189-1202.

  54. (with J. Gonzalo) Fifteen years of contact circles and contact spheres,
    Acta Math. Vietnam. 38 (2013), 145-164.

  55. (with K. Zehmisch) How to recognize a 4-ball when you see one,
    Münster J. Math. 6 (2013), 525-554, erratum: pp. 555-556.

  56. Contact manifold,
    Bull. Man. Atl. (2013)

  57. (with M. Dörner and K. Zehmisch) Open books and the Weinstein conjecture,
    Q. J. Math. 65 (2014), 869-885.

  58. (with N. Röttgen and K. Zehmisch) Trapped Reeb orbits do not imply periodic ones,
    Invent. Math. 198 (2014), 211-217.

  59. (with M. Klukas) The fundamental group of the space of contact structures on the 3-torus,
    Math. Res. Lett. 21 (2014), 1257-1262.

  60. (with S. Onaran) Legendrian rational unknots in lens spaces,
    J. Symplectic Geom. 13 (2015), 17-50.

  61. C. K. Boese, P. Lechler, L. Rose, J. Dargel, J. Oppermann, P. Eysel, H. Geiges and J. Bredow,
    Calibration markers for digital templating in total hip arthroplasty,
    PLoS ONE 10(7): e0128529 (2015).

  62. (with K. Zehmisch) Reeb dynamics detects odd balls,
    Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 15 (2016), 663-681.

  63. (with K. Zehmisch) The Weinstein conjecture for connected sums,
    Int. Math. Res. Not. IMRN (2016), no. 2, 325-342.

  64. C. K. Boese, J. Bredow, J. Dargel, P. Eysel, H. Geiges and P. Lechler,
    Calibration marker position in digital templating of total hip arthroplasty,
    The Journal of Arthroplasty 31 (2016), 883-887.

  65. (with N. Röttgen and K. Zehmisch) From a Reeb orbit trap to a Hamiltonian plug,
    Arch. Math. (Basel) 107 (2016), 397-404.

  66. (with J. Gonzalo) Transversely holomorphic flows and contact circles on spherical 3-manifolds,
    Enseign. Math. (2) 62 (2016), 527-567.

  67. (with K. Zehmisch) Cobordisms between symplectic fibrations,
    Manuscripta Math. 153 (2017), 331-340.

  68. How to depict 5-dimensional manifolds,
    Jahresber. Dtsch. Math.-Ver. 119 (2017), 221-247.

  69. (with M. Dörner and K. Zehmisch) Finsler geodesics, periodic Reeb orbits, and open books,
    Eur. J. Math. 3 (2017), 1058-1075.

  70. (with F. Ding and G. Zhang) On subcritically Stein fillable 5-manifolds,
    Canad. Math. Bull. 61 (2018), 85-96.

  71. Isotopies vis-à-vis level-preserving embeddings,
    Arch. Math. (Basel) 110 (2018), 197-200.

  72. (with P. Albers and K. Zehmisch) Reeb dynamics inspired by Katok's example in Finsler geometry,
    Math. Ann. 370 (2018), 1883-1907.

  73. (with C. Lange) Seifert fibrations of lens spaces,
    Abh. Math. Semin. Univ. Hambg. 88 (2018), 1-22.

  74. (with S. Onaran) Legendrian lens space surgeries,
    Michigan Math. J. 67 (2018), 405-422.

  75. (with S. Durst and M. Kegel) Handle homology of manifolds,
    Topology Appl. 256 (2019), 113-127.

  76. Controlled Reeb dynamics - Three lectures not in Cala Gonone,
    Complex Manifolds 6 (2019), 118-137.

  77. (with K. Barth and K. Zehmisch) The diffeomorphism type of symplectic fillings,
    J. Symplectic Geom. 17 (2019), 929-971.

  78. (with K. Zehmisch) Odd-symplectic forms via surgery and minimality in symplectic dynamics,
    Ergodic Theory Dynam. Systems 40 (2020), 699-713.

  79. (with S. Durst, J. Gonzalo and M. Kegel) Parallelisability of 3-manifolds via surgery,
    Expo. Math. 38 (2020), 131-137.

  80. (with S. Onaran) Exceptional Legendrian torus knots,
    Int. Math. Res. Not. IMRN (2020), no. 22, 8786-8817.

  81. (with S. Onaran) Legendrian Hopf links,
    Q. J. Math. 71 (2020), 1419-1459.

  82. (with T. Becker) The contact structure induced by a line fibration of R3 is standard,
    Bull. London Math. Soc. 53 (2021), 104-107.

  83. (with K. Sporbeck and K. Zehmisch) Subcritical polarisations of symplectic manifolds have degree one,
    Arch. Math. (Basel) 117 (2021), 227-231.

  84. (with C. Lange) Correction to: Seifert fibrations of lens spaces,
    Abh. Math. Semin. Univ. Hambg. 91 (2021), 145-150.

  85. (with B. Albach) Surfaces of section for Seifert fibrations,
    Arnold Math. J. 7 (2021), 573-597.

  86. (with P. Albers and K. Zehmisch) Pseudorotations of the 2-disc and Reeb flows on the 3-sphere,
    Ergodic Theory Dynam. Systems 42 (2022), 402-436.

  87. What does a vector field know about volume?,
    J. Fixed Point Theory Appl. 24 (2022), Paper No. 23.

  88. (with M. Kwon and K. Zehmisch) Diffeomorphism type of symplectic fillings
    of unit cotangent bundles,
    J. Topol. Anal. 15 (2023), 683-705.

  89. (with P. Albers and K. Zehmisch) A symplectic dynamics proof of the degree-genus formula,
    Arnold Math. J. 9 (2023), 41-68.

  90. (with N. Thies) Klein bottles in lens spaces,
    Involve 16 (2023), 621-636.

  91. (with M. Sağlam and K. Zehmisch) Why bootstrapping for J-holomorphic curves fails in Ck,
    Anal. Math. Phys. 13 (2023), Paper No. 11, 11 pp.

  92. (with J. Hedicke and M. Sağlam) Bott-integrable Reeb flows on 3-manifolds,
    J. London Math. Soc. (2) 109 (2024), Paper No. e12859, 42 pp.

  93. (with K. Zehmisch) Symplectic fillings of unit cotangent bundles of hyperbolic surfaces,
    Israel J. Math., to appear.

Book chapter:
  1. Contact Geometry (pdf),
    in: Handbook of Differential Geometry vol. 2
    (F.J.E. Dillen and L.C.A. Verstraelen, eds.), North-Holland, Amsterdam (2006), 315-382.

Non-refereed contributions to conference proceedings:
  1. (with J. Gonzalo) Topology and analysis of contact circles,
    in: Contact and Symplectic Geometry (C. B. Thomas, ed.),
    Cambridge University Press (1996), 66-77.

  2. (with C. B. Thomas) Contact structures on 7-manifolds,
    CRM Proc. Lecture Notes 15 (1998), 53-67.

  3. Contact topology in dimension greater than three,
    in: Proc. European Congress of Mathematics (Barcelona, 2000),
    Progress in Math. 202, Birkhäuser, Basel (2001), 535-545.

  4. Contact Dehn surgery, symplectic fillings, and Property P for knots,
    in: Arbeitstagung 2005, Max-Planck-Institut für Mathematik, Bonn,
    MPIM Preprint Series 60 (2005), 7 pages.

  5. (with F. Ding) Examples of Legendrian knots and links classified by classical invariants,
    in: Proceedings of the Second East Asian School of Knots and Related Topics in Geometric Topology
    (Dalian, China, 2005), 21-24.

  6. (with K. Zehmisch) Cerf's theorem and other applications of the filling with holomorphic discs,
    Oberwolfach Reports 8 (2011), 1055-1056.

  7. (with N. Röttgen and K. Zehmisch) Trapped Reeb orbits do not imply periodic ones,
    Oberwolfach Reports 12 (2015), 1955-1957.

Preprints:
  1. (with R. Chatterjee and S. Onaran) Legendrian Hopf links in L(p,1) (2024).

Lecture notes:
  1. h-Principles and Flexibility in Geometry,
    Lectures given in the Graduiertenkolleg `Analysis, Geometrie
    und ihre Verbindung zu den Naturwissenschaften',
    Universität Leipzig, December 2000
    (identical with no. 28).

Book reviews published in The Times Higher Education Supplement:
  1. The fickle fortune of some fine figures,
    Review of Oxford Figures: 800 Years of the Mathematical Sciences by J. Fauvel et al.,
    12 January, 2001.

  2. The list that sent mathematicians for their pencils,
    Review of The Hilbert Challenge by J. Gray,
    9 March, 2001.

  3. No need for leopard skin, just an Indian rope trick,
    Review of 1089 and All That by D. Acheson,
    14 March, 2003.

  4. Hopefully not the last word on infinity,
    Review of A Brief History of Infinity by B. Clegg
    and Everything and More by D. F. Wallace,
    13 August, 2004.

  5. Signs of success clear and obscure,
    Review of John Pell (1611-1685) and His Correspondence with Sir Charles Cavendish
    by N. Malcolm and J. Stedall,
    5 August, 2005.

  6. Wake up to a long-dormant Dutch titan,
    Review of Huygens - The Man Behind the Principle by C. D. Andriesse,
    13 January, 2006.

  7. Questions of cultural superiority can muddle mathematical thinking,
    Review of A History of Mathematics by L. Hodgkin,
    29 September, 2006.

Other publications:
  1. 254 reviews for Mathematical Reviews, 1993-2018.

  2. Facets of the cultural history of mathematics,
    Inaugural lecture, Universiteit Leiden (1999).

  3. Several articles (e.g. on contact surgery and h-principle) in
    Encyclopaedia of Mathematics, suppl. II (M. Hazewinkel, ed.), Kluwer, Dordrecht (2000).

  4. Een eeuw wiskunde in boeken: Anything by Adams or Milnor,
    Nieuw Archief voor Wiskunde (5) 1 (2000), p. 308.

Last updated 23 August 2024