Graphs, links, and duality on surfaces
Robust 4-manifolds and robust embeddings
(with Paul Fendley) Link invariants, the chromatic polynomial and the Potts model, to appear in Advances in Theoretical and Mathematical Physics.
(with Paul Fendley) Tutte chromatic identities from the Temperley-Lieb algebra, Geom. Topol. 13(2009), 709-741.
A counterexample to the strong version of Freedman’s conjecture, Ann. of Math. 168 (2008), 675-693.
Link groups and the A-B slice problem, Topology and Physics, Proceedings of the International conference
in memory of X.-S. Lin, World Sci. Publ. 2008, 203-218.
(with Michael Freedman) On the asymptotics of quantum SU(2)
representations of mapping class groups, Forum Math. 18 (2006), 293-304.
Surgery and involutions on 4-manifolds, Algebr. Geom. Topol. 5 (2005), 1719-1732.
Surfaces
in 4-manifolds and the surgery conjecture, Proceedings of the Fields
Institute/McMaster Conference on Geometry and Topology of Manifolds. AMS, 2005.
Dwyer's filtration and
topology of 4-manifolds, Math. Res. Lett.
10 (2003), 247-251.
On disk embedding
up to s-cobordism, arXiv:math.GT/0209273.
(with Ronnie Lee)
Surgery on closed 4-manifolds with free fundamental group, Math. Proc. Cambridge Philos. Soc. 133
(2002), 305--310.
Exponential
separation in 4-manifolds, Geom. Topol. 4 (2000), 397-405.
(with Frank Quinn) Subexponential
groups in 4-manifold topology, Geom. Topol. 4
(2000), 407-430.
Embedding
obstructions and 4-dimensional thickenings of 2-complexes, Proc. Amer. Math. Soc. 128 (2000), 3683-3691.
On the Relative Slice
Problem and Four Dimensional Topological Surgery, Math. Ann. 315 (1999),
363-396.
Additivity properties of Milnor's m-invariants, J. Knot Theory Ramifications 7 (1998), 625-637.
(with Peter Teichner)
Alexander
duality, gropes and link homotopy, Geom. Topol. 1 (1997), 51-69.
(with Michael Freedman) Notes on ends of hyperbolic
3-manifolds, Proceedings of the 13th Annual Workshop in Geometric
Topology (1996), 1-15.
(with Michael Freedman and Peter Teichner)
Van Kampen's
embedding obstruction is incomplete for 2-complexes in R4 ,
Math. Res. Lett. 1 (1994), 167-176.
Research was partially supported by the NSF.