33 citations · 168 across the 48 of their papers we have counts for
7 papers · 1 filter
The length of unknotting tunnels
Daryl Cooper, Marc Lackenby, Jessica S. Purcell
We show there exist tunnel number one hyperbolic 3-manifolds with arbitrarily long unknotting tunnel. This provides a negative answer to an old question of Colin Adams.
Spectral geometry, link complements and surgery diagrams
Marc Lackenby
We provide an upper bound on the Cheeger constant and first eigenvalue of the Laplacian of a finite-volume hyperbolic 3-manifold M, in terms of data from any surgery diagram for M.…
Unknotting genus one knots
Alexander Coward, Marc Lackenby
For any knot with genus one and unknotting number one, other than the figure-eight knot, we prove that there is exactly one way to unknot it by means of a crossing change. In the c…
The maximal number of exceptional Dehn surgeries
Marc Lackenby, Robert Meyerhoff
We prove two conjectures of C. Gordon. We show that the maximal number of exceptional Dehn surgeries on a 1-cusped hyperbolic 3-manifold is 10, and that the maximal intersection nu…
The crossing number of composite knots
Marc Lackenby
It is a very old conjecture that the crossing number of knots is additive under connected sum. In other words, if K#K' is the connected sum of knots K and K', then does the equalit…
LERF and the Lubotzky-Sarnak conjecture
M. Lackenby, D. D. Long, A. W. Reid
We prove that every closed hyperbolic 3-manifold has a family of (possibly infinite sheeted) coverings with the property that the Cheeger constants in the family tend to zero. This…