Publications of Hansjörg Geiges
Books:

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

The Geometry of Celestial Mechanics,
London Mathematical Society Student Texts 83,
Cambridge University Press (2016).
Refereed articles:

Contact structures on 1connected 5manifolds,
Mathematika 38 (1991), 303311.

Symplectic structures on T^{2}bundles over T^{2},
Duke Math. J. 67 (1992), 539555.

Contact structures on (n1)connected (2n+1)manifolds,
Pacific J. Math. 161 (1993), 129137.

Symplectic manifolds with disconnected boundary of contact type,
Int. Math. Res. Not. IMRN (1994), no. 1, 2330.

(with C. B. Thomas) Hypercontact manifolds,
J. London Math. Soc. (2) 51 (1995), 342352.

Examples of symplectic 4manifolds with disconnected boundary
of contact type,
Bull. London Math. Soc. 27 (1995), 278280.

(with J. Gonzalo) Contact geometry and complex surfaces,
Invent. Math. 121 (1995), 147209.

(with J. Gonzalo) Seifert invariants of leftquotients of 3dimensional
simple Lie groups,
Topology Appl. 66 (1995), 117127.

(with J. Gonzalo) An application of convex integration to
contact geometry,
Trans. Amer. Math. Soc. 348 (1996), 21392149.

Symplectic couples on 4manifolds,
Duke Math. J. 85 (1996), 701711.

Constructions of contact manifolds,
Math. Proc. Cambridge Philos. Soc. 121 (1997), 455464.

Normal contact structures on 3manifolds,
Tôhoku Math. J. 49 (1997), 415422.

(with J. Gonzalo) Contact circles on 3manifolds,
J. Differential Geom. 46 (1997), 236286.

Mannigfaltige Geometrien,
Elem. Math. 52 (1997), 93107.

Applications of contact surgery,
Topology 36 (1997), 11931220.

(with C. B. Thomas) Contact topology and the structure of 5manifolds
with fundamental group Z_{2},
Ann. Inst. Fourier (Grenoble) 48 (1998), 11671188.

(with C. B. Thomas) Almost linear actions by finite groups on
S^{2n1},
in: Proceedings of the Kirbyfest (J. Hass, M. Scharlemann, eds.),
Geom. Topol. Monogr. 2 (1999), 135156.

(with D. Rattaggi) Periodic automorphisms of surfaces: Invariant
circles and maximal orders,
Experiment. Math. 9 (2000), 7584.

(with S. Müller) Almost complex structures on 8manifolds,
Enseign. Math. (2) 46 (2000), 95107.

Facets of the cultural history of mathematics,
European Review 8 (2000), 487497.

(with C. B. Thomas) Finite group actions on the 7sphere,
Enseign. Math. (2) 46 (2000), 403410.

Chern numbers of almost complex manifolds,
Proc. Amer. Math. Soc. 129 (2001), 37493752.

A brief history of contact geometry and topology,
Expo. Math. 19 (2001), 2553;
Chinese translation in Shuxue Yilin 25 (2006), 133148.

(with C. B. Thomas) Contact structures, equivariant spin bordism,
and periodic fundamental groups,
Math. Ann. 320 (2001), 685708.

(with F. Ding) Symplectic fillability of tight contact structures
on torus bundles,
Algebr. Geom. Topol. 1 (2001), 153172.

Beweis des Satzes von Morley nach A. Connes,
Elem. Math. 56 (2001), 137142.

(with J. Gonzalo) Moduli of contact circles,
J. Reine Angew. Math. 551 (2002), 4185.

hPrinciples and Flexibility in Geometry,
Mem. Amer. Math. Soc. 164 (2003), no. 779.

(with F. Ding) A Legendrian surgery presentation of contact 3manifolds,
Math. Proc. Cambridge Philos. Soc. 136 (2004), 583598.

(with J. Gonzalo) On the topology of the space of contact structures
on torus bundles,
Bull. London Math. Soc. 36 (2004), 640646.

(with F. Ding and A. I. Stipsicz) Surgery diagrams for contact 3manifolds,
Turkish J. Math. 28 (2004), 4174
(Proceedings of the 10th Gökova GeometryTopology
conference, 2003).

(with F. Ding) E_{8}plumbings and exotic contact
structures on spheres,
Int. Math. Res. Not. IMRN (2004), no. 71, 38253837.

(with F. Ding and A. I. Stipsicz) Lutz twist and contact surgery,
Asian J. Math. 9 (2005), 5764.

Christiaan Huygens and contact geometry,
Nieuw Arch. Wiskd. (5) 6 (2005), 117123;
reprinted in Newsletter European Math. Soc. 65 (September 2007), 1319.

Contact Dehn surgery, symplectic fillings, and Property P for knots,
Expo. Math. 24 (2006), 273280.

(with F. Ding) Legendrian knots and links classified by classical
invariants,
Commun. Contemp. Math. 9 (2007), 135162.

(with F. Pasquotto) A formula for the Chern classes of symplectic
blowups,
J. London Math. Soc. (2) 76 (2007), 313330.

(with F. Ding) A unique decomposition theorem for tight contact
3manifolds,
Enseign. Math. (2) 53 (2007), 333345.

Horizontal loops in Engel space,
Math. Ann. 342 (2008), 291296.

A contact geometric proof of the WhitneyGraustein theorem,
Enseign. Math. (2) 55 (2009), 93102.

(with J. Gonzalo) Contact spheres and hyperkähler geometry,
Comm. Math. Phys. 287 (2009), 719748.

(with F. Ding) Handle moves in contact surgery diagrams,
J. Topol. 2 (2009), 105122.

(with A. I. Stipsicz) Contact structures on product fivemanifolds
and fibre sums along circles,
Math. Ann. 348 (2010), 195210.

(with F. Ding) The diffeotopy group of S^{1}× S^{2}
via contact topology,
Compos. Math. 146 (2010), 10961112.

(with F. Ding) Legendrian helix and cable links,
Commun. Contemp. Math. 12 (2010), 487500.

(with J. Gonzalo) A homogeneous GibbonsHawking ansatz and
Blaschke products,
Adv. Math. 225 (2010), 25982615.

(with K. Zehmisch) Eliashberg's proof of Cerf's theorem,
J. Topol. Anal. 2 (2010), 543579.

(with F. Ding) Neighbourhoods and isotopies of knots in contact
3manifolds,
Arch. Math. (Basel) 97 (2011), 391397.

Contact structures and geometric topology,
in: Global Differential Geometry, Springer Proc. Math. 17,
SpringerVerlag, Berlin (2012), 463489.

(with J. Gonzalo) Generalised spin structures on 2dimensional
orbifolds,
Osaka J. Math. 49 (2012), 449470.

(with K. Zehmisch) Symplectic cobordisms and the strong Weinstein
conjecture,
Math. Proc. Cambridge Philos. Soc. 153 (2012), 261279.

(with F. Ding and O. van Koert) Diagrams for contact 5manifolds,
J. London Math. Soc. (2) 86 (2012), 657682.

(with F. Ding) Contact structures on principal circle bundles,
Bull. London Math. Soc. 44 (2012), 11891202.

(with J. Gonzalo) Fifteen years of contact circles and contact spheres,
Acta Math. Vietnam. 38 (2013), 145164.

(with K. Zehmisch) How to recognize a 4ball when you see one,
Münster J. Math. 6 (2013), 525554, erratum: pp. 555556.

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

(with M. Dörner and K. Zehmisch) Open books and the Weinstein
conjecture,
Q. J. Math. 65 (2014), 869885.

(with N. Röttgen and K. Zehmisch) Trapped Reeb orbits do not
imply periodic ones,
Invent. Math. 198 (2014), 211217.

(with M. Klukas) The fundamental group of the space of contact structures
on the 3torus,
Math. Res. Lett. 21 (2014), 12571262.

(with S. Onaran) Legendrian rational unknots in lens spaces,
J. Symplectic Geom. 13 (2015), 1750.

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).

(with K. Zehmisch) Reeb dynamics detects odd balls,
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 15 (2016), 663681.

(with K. Zehmisch) The Weinstein conjecture for connected sums,
Int. Math. Res. Not. IMRN (2016), no. 2, 325342.

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), 883887.

(with N. Röttgen and K. Zehmisch) From a Reeb orbit trap to
a Hamiltonian plug,
Arch. Math. (Basel) 107 (2016), 397404.

(with J. Gonzalo) Transversely holomorphic flows and contact circles
on spherical 3manifolds,
Enseign. Math. (2) 62 (2016), 527567.

(with K. Zehmisch) Cobordisms between symplectic fibrations,
Manuscripta Math. 153 (2017), 331340.

How to depict 5dimensional manifolds,
Jahresber. Dtsch. Math.Ver. 119 (2017), 221247.

(with M. Dörner and K. Zehmisch) Finsler geodesics, periodic Reeb
orbits, and open books,
Eur. J. Math. 3 (2017), 10581075.

(with F. Ding and G. Zhang) On subcritically Stein fillable 5manifolds,
Canad. Math. Bull. 61 (2018), 8596.

Isotopies visàvis levelpreserving embeddings,
Arch. Math. (Basel) 110 (2018), 197200.

(with P. Albers and K. Zehmisch) Reeb dynamics inspired by Katok's example
in Finsler geometry,
Math. Ann. 370 (2018), 18831907.

(with C. Lange) Seifert fibrations of lens spaces,
Abh. Math. Semin. Univ. Hambg. 88 (2018), 122.

(with S. Onaran) Legendrian lens space surgeries,
Michigan Math. J. 67 (2018), 405422.

(with S. Durst and M. Kegel) Handle homology of manifolds,
Topology Appl. 256 (2019), 113127.

Controlled Reeb dynamics  Three lectures not in Cala Gonone,
Complex Manifolds 6 (2019), 118137.

(with K. Barth and K. Zehmisch) The diffeomorphism type of
symplectic fillings,
J. Symplectic Geom. 17 (2019), 929971.

(with K. Zehmisch) Oddsymplectic forms via surgery and minimality in
symplectic dynamics,
Ergodic Theory Dynam. Systems 40 (2020), 699713.

(with S. Durst, J. Gonzalo and M. Kegel) Parallelisability of 3manifolds
via surgery,
Expo. Math. 38 (2020), 131137.

(with S. Onaran) Exceptional Legendrian torus knots,
Int. Math. Res. Not. IMRN (2020), no. 22, 87868817.

(with T. Becker) The contact structure induced by a line fibration of
R^{3} is standard,
Bull. Lond. Math. Soc., to appear.

(with P. Albers and K. Zehmisch) Pseudorotations of the 2disc and Reeb flows
on the 3sphere,
Ergodic Theory Dynam. Systems, to appear.

What does a vector field know about volume?,
J. Fixed Point Theory Appl., to appear.

(with S. Onaran) Legendrian Hopf links,
Q. J. Math., to appear.
Book chapter:

Contact Geometry (pdf),
in: Handbook of Differential Geometry vol. 2
(F.J.E. Dillen and L.C.A. Verstraelen, eds.),
NorthHolland, Amsterdam (2006), 315382.
Nonrefereed contributions to conference proceedings:

(with J. Gonzalo) Topology and analysis of contact circles,
in: Contact and Symplectic Geometry (C. B. Thomas, ed.),
Cambridge University Press (1996), 6677.

(with C. B. Thomas) Contact structures on 7manifolds,
CRM Proc. Lecture Notes 15 (1998), 5367.

Contact topology in dimension greater than three,
in: Proc. European Congress of Mathematics (Barcelona, 2000),
Progress in Math. 202, Birkhäuser, Basel (2001), 535545.

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

(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), 2124.

(with K. Zehmisch) Cerf's theorem and other applications of the filling
with holomorphic discs,
Oberwolfach Reports 8 (2011), 10551056.

(with N. Röttgen and K. Zehmisch) Trapped Reeb orbits do not
imply periodic ones,
Oberwolfach Reports 12 (2015), 19551957.
Preprints:

(with P. Albers and K. Zehmisch) A symplectic dynamics proof of the
degreegenus formula (2019).

(with M. Kwon and K. Zehmisch) Diffeomorphism type of symplectic fillings
of unit cotangent bundles (2019).

(with C. Lange) Seifert fibrations of lens spaces over nonorientable bases
(2020).

Lecture notes:

hPrinciples 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:

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.

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

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

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.

Signs of success clear and obscure,
Review of John Pell (16111685) and
His Correspondence with Sir Charles Cavendish
by N. Malcolm and J. Stedall,
5 August, 2005.

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

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

254 reviews for Mathematical Reviews, 19932018.

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

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

Een eeuw wiskunde in boeken:
Anything by Adams or Milnor,
Nieuw Archief voor Wiskunde (5) 1 (2000), p. 308.
Last updated 26 November 2020