Marc Lackenby

Research interests: Topology, geometry & group theory

Editor of 'Journal of Topology'
Editor of 'Groups, Geometry and Dynamics'
Editor of 'Journal of the London Mathematical Society'

Mathematical Institute office: T3
Phone (Institute): 01865 273561
Phone (College): 01865 271728
Email: lackenby(at)maths.ox.ac.uk

My CV (April 2013)

• 1. The Whitney trick , Topology and Its Applications 71 (1996) 115-118.
• 2. Fox's congruence classes and the quantum-SU(2) invariants of links in 3-manifolds, Comment. Math. Helv. 71 (1996) 664-677.
• 3. Surfaces, surgery and unknotting operations, Math. Ann. 308 (1997) 615-632.
• 4. Dehn surgery on knots in 3-manifolds, J. Amer. Math. Soc. 10 (1997) 835-864.
• 5. Upper bounds in the theory of unknotting operations, Topology 37 (1998) 63-73.
• 6. (With Daryl Cooper) Dehn surgery and negatively curved 3-manifolds, J. Differential Geom. 50 (1998) 591-624. (PS) (PDF)
• 7. Word hyperbolic Dehn surgery, Invent. Math. 140 (2000) 243-282. (PS) (PDF)
• 8. Taut ideal triangulations of 3-manifolds, Geom. Top. 4 (2000) 369-395. (PS) (PDF)
• 9. Attaching handlebodies to 3-manifolds, Geom. Top. 6 (2002) 889-904. (PS) (PDF)
• 10. Exceptional surgery curves in triangulated 3-manifolds, Pacific J. Math. 210 (2003), 101-163. (PS) (PDF)
• 11. The canonical decomposition of once-punctured torus bundles, Comment. Math. Helv. 78 (2003) 363-384. (PS) (PDF)
• 12. The volume of hyperbolic alternating link complements Proc. London Math. Soc. 88 (2004) 204-224 (PS) (PDF)
• 13. The asymptotic behaviour of Heegaard genus Math. Res. Lett. 11 (2004) 139-149 (PS) (PDF)
• 14. The Heegaard genus of amalgamated 3-manifolds Geom. Dedicata 109 (2004) 139-145 (PS) (PDF)
• 15. A characterisation of large finitely presented groups J. Algebra 287 (2005) 458-473 (PS) (PDF)
• 16. Expanders, rank and graphs of groups Israel J. Math. 146 (2005) 357-370 (PS) (PDF)
• 17. Classification of alternating knots with tunnel number one Comm. Anal. Geom. 13 (2005) 151-186 (PS) (PDF)
• 18. Heegaard splittings, the virtually Haken conjecture and Property (tau), Invent. Math. 164 (2006) 317-359 (PS) (PDF)
• 19. Covering spaces of 3-orbifolds Duke Math J. 136 (2007) 181-203 (PS) (PDF)
• 20. Some 3-manifolds and 3-orbifolds with large fundamental group Proc. Amer. Math. Soc. 135 (2007) 3393-3402 (PS) (PDF)
• 21. Adding high powered relations to large groups Math. Res. Lett. 14 (2007) 983-993 (PS) (PDF)
• 22. (With Darren Long and Alan Reid) Covering spaces of arithmetic 3-orbifolds Int. Math. Res. Not. (2008) (PS) (PDF)
• 23. An algorithm to determine the Heegaard genus of simple 3-manifolds with non-empty boundary Alg. Geom. Top. 8 (2008) 911-934 (PS) (PDF)
• 24. (With Darren Long and Alan Reid) LERF and the Lubotzky-Sarnak conjecture Geom. Topol. 12 (2008) 2047-2056 (PS) (PDF)
• 25. New lower bounds on subgroup growth and homology growth Proc. London Math. Soc. 98 (2009) 271-297. (PS) (PDF)
• 26. Large groups, Property (tau) and the homology growth of subgroups Math. Proc. Camb. Phil. Soc. 146 (2009) 625-648 (PS) (PDF)
• 27. The crossing number of composite knots J. Topology 2 (2009) 747-768. (PS) (PDF)
• 28. Surface subgroups of Kleinian groups with torsion Invent. Math. 179 (2010) 175-190. (PS) (PDF)
• 29. (with Daryl Cooper and Jessica Purcell) The length of unknotting tunnels Alg. Geom. Top. 10 (2010) 637-661. (PDF)
• 30. Spectral geometry, link complements and surgery diagrams Geom. Dedicata 147 (2010) 191-206. (PS) (PDF)
• 31. Detecting large groups J. Algebra 324 (2010) 2636-2657. (PS) (PDF)
• 32. (with Alexander Coward) Unknotting genus one knots Comment. Math. Helv. 86 (2011) 383-399. (PS) (PDF)
• 33. Finite covering spaces of 3-manifolds Proceedings of the ICM, Volume II, 1042-1070, Hindustan Book Agency, New Delhi, 2010 (PDF)
• 34. (with Robert Meyerhoff) The maximal number of exceptional Dehn surgeries Invent. Math. 191 (2013) 341-382. (PS) (PDF)
            The main theorems of this paper have a computer-assisted proof. The relevant C++ routines are below:
               slopes1.cpp
               slopes2.cpp
               slopes3.cpp
               slopes4.cpp
               slopes5.cpp
               myDouble.h
               myDouble.cpp
  
• 35. (With Alexander Coward) An upper bound on Reidemeister moves Amer. J. Math. (to appear) (PS) (PDF)
• 36. Core curves of triangulated solid tori Trans. Amer. Math. Soc. (to appear) (PDF)

• 37. The crossing number of satellite knots (PS) (PDF)
• 38. Finding disjoint surfaces in 3-manifolds (PDF)
• 39. A polynomial upper bound on Reidemeister moves (PDF)
• 40. (with Jessica Purcell) Geodesics and compression bodies (PS) (PDF)

Some documents by my students

• Homology in finite index subgroups, PhD thesis by Liam Wall, January 2010
• Constructing the Cayley graphs of F_d/D_n^p(F_d), Summer project by Henry Bradford, September 2010

Some of my talks

Scottish Topology Seminar / Swiss Knots, Spring 2013

• A polynomial upper bound on Reidemeister moves

Clay Mathematics Conference, June 2012

• The Dehn surgery problem

LMS Poincare anniversary meeting, May 2012

• The Poincare conjecture

Talk at Fritz Grunewald's 60th birthday conference, April 2009

• Surface subgroups of arithmetic Kleinian groups

4 Talks at Gottingen, Autumn School on Geometric Group Theory, November 2008

• Surface subgroups in dimension 3, I
• Surface subgroups in dimension 3, II
• Surface subgroups in dimension 3, III
• Surface subgroups in dimension 3, IV

Talk at Thurston's 60th birthday conference, June 2007

• The crossing number of composite knots

3 Talks at Oxford, Hilary Term 2007

• The geometry and topology of finite index subgroups, I
• The geometry and topology of finite index subgroups, II
• The geometry and topology of finite index subgroups, III

3 Talks at the Institute of Advanced Study, Princeton
Workshop on Lie Groups, Representations and Discrete Mathematics,
14-18 November 2005


Property (tau) and Geometry, I, was given by Alex Lubotzky
• Property (tau) and Geometry, II
• Property (tau) and Geometry, III
• Property (tau) and Geometry, IV

3 Talks at the ICMS, Edinburgh, "3-Manifolds after Perelman", 13-17 March 2006

• Finite covers of 3-manifolds, I
• Finite covers of 3-manifolds, II
• Finite covers of 3-manifolds, III

Lecture Notes and Problem Sheets

Topology & Groups, Michaelmas 2008 (updated October 2011)

• Lecture notes (PS) (PDF)
• Problem Sheet 1 (PS) (PDF)
• Problem Sheet 2 (PS) (PDF)
• Problem Sheet 3 (PS) (PDF)
• Problem Sheet 4 (PS) (PDF)
• Problem Sheet 5 (PS) (PDF)
• Problem Sheet 6 (PS) (PDF)
• Problem Sheet 7 (PS) (PDF)

Section c Algebraic Topology, Hilary 2001

• Question Sheet 1
• Question Sheet 2
• Question Sheet 3
• Question Sheet 4
• Question Sheet 5
• Question Sheet 6
• Question Sheet 7

Three-dimensional manifolds (Graduate Course, Michaelmas 1999)

• Chapters 1 and 2
• Chapter 3
• Chapters 4 and 5
• Chapters 6 and 7
• Chapters 8 to 12
• Examples Sheet 1
• Examples Sheet 2

Hyperbolic manifolds (Graduate Course, Hilary 2000)

• Introductory chapter on Riemannian manifolds (Very brief!) (PS) (PDF)
• Chapters 0 - 5 (PS) (PDF)
• Chapters 6 - 11 (PS) (PDF)
• Example Sheet 1 (from Part III course) (PS) (PDF)
• Example Sheet 2 (from Part III course) (PS) (PDF)

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