The Gromov Invariant of Links.
The Hauptvermutung for homeomorphisms II. A proof valid for open 4-manifolds
The Heegaard genus of manifolds obtained by surgery on links and knots.
The homeomorphism group of a three-dimensional polyhedron is locally contractible
The Homflypt skein module of a connected sum of 3-manifolds.
The homotopy dimension of codiscrete subsets of the 2-sphere 𝕊²
Andreas Zastrow conjectured, and Cannon-Conner-Zastrow proved, that filling one hole in the Sierpiński curve with a disk results in a planar Peano continuum that is not homotopy equivalent to a 1-dimensional set. Zastrow's example is the motivation for this paper, where we characterize those planar Peano continua that are homotopy equivalent to 1-dimensional sets. While many planar Peano continua are not homotopy equivalent to 1-dimensional compacta, we prove that each has fundamental group that...
The incidence submanifold of for odd is nonorientable
The ...-injectivity of self-maps of nonzero degree on 3-manifolds.
The isomorphism problem for toral relatively hyperbolic groups
We provide a solution to the isomorphism problem for torsion-free relatively hyperbolic groups with abelian parabolics. As special cases we recover solutions to the isomorphism problem for: (i) torsion-free hyperbolic groups (Sela, [60] and unpublished); and (ii) finitely generated fully residually free groups (Bumagin, Kharlampovich and Miasnikov [14]). We also give a solution to the homeomorphism problem for finite volume hyperbolic -manifolds, for . In the course of the proof of the main result,...
The Jones-Witten invariants of knots
The Kauffman bracket skein module of S1 x S2.
The Kazhdan property of the mapping class group of closed surfaces and the first cohomology group of its cofinite subgroups.
The Lie affine foliations on 4-manifolds.
The minimum dimension of a residual ANR
The Nielsen coincidence theory on topological manifolds
We generalize the coincidence semi-index introduced in [D-J] to pairs of maps between topological manifolds. This permits extending the Nielsen theory to this class of maps.
The Novikov conjecture and low-dimensional topology.
The ?-orbifold Group of a Link.
The -central extension of the Mapping Class Group of orientable surfaces
Topological Quantum Field Theories are closely related to representations of Mapping Class Groups of surfaces. Considering the case of the TQFTs derived from the Kauffman bracket, we describe the central extension coming from this representation, which is just a projective extension.
The recognition problem for topological manifolds
The regular projective solution space of the figure-eight knot complement.