A conjecture on Khovanov's invariants
We formulate a conjectural formula for Khovanov's invariants of alternating knots in terms of the Jones polynomial and the signature of the knot.
A construction of a CW-decomposition of s-cubes which are manifolds
A construction of noncontractible simply connected cell-like two-dimensional Peano continua
Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts from a noncontractible n-dimensional Peano continuum for any n > 0, then our construction yields a simply connected noncontractible (n + 1)-dimensional cell-like Peano continuum. In particular, starting from the circle 𝕊¹,...
A contribution to the topological classification of the spaces Ср(X)
We prove that for each countably infinite, regular space X such that is a -space, the topology of is determined by the class of spaces embeddable onto closed subsets of . We show that , whenever Borel, is of an exact multiplicative class; it is homeomorphic to the absorbing set for the multiplicative Borel class if . For each ordinal α ≥ 2, we provide an example such that is homeomorphic to .
A correction of two papers concerning Hilbert manifolds
A correction to a paper of H. King.
A correction to my paper:"Some topological extensions of plane geometry"
A corrigendum to the paper “Connecting direct limit topologies with metrics on infinite-dimensional manifolds”
A countable dense homogeneous space with a dense rigid open subspace
We show that there is a Polish space which is countable dense homogeneous but contains a dense open rigid connected subset. This answers several questions of Fitzpatrick and Zhou.
A criterion for homeomorphism between closed Haken manifolds.
A criterion for the noncellularity of arcs
A decomposition into homeomorphic handlebodies with naturally equivalent involutions.
A decomposition theorem for h-cobordant smooth simply-connected compact 4-manifolds.
A filtration of the set of integral homological 3-spheres.
A finite graphic calculus for 3-manifolds.
A gauge-field approach to 3- and 4-manifold invariants
An approach to construction of topological invariants of the Reshetikhin-Turaev-Witten type of 3- and 4-dimensional manifolds in the framework of SU(2) Chern-Simons gauge theory and its hidden (quantum) gauge symmetry is presented.
A general approximation theorem for Hilbert cube manifolds
A generalized bridge number for links in 3-manifolds.
A geometric invariant of discrete groups.
A Group with Torsion-Free 2-Divisible Homology and Cappell's Result on the Novikov Conjecture.