A lower bound to the action dimension of a group.
A mapping theorem for infinite-dimensional manifolds and its generalizations
A mapping theorem for topological sigma-compact manifolds
A Maximal Toroidal Graph which is not a Triangulation.
A Model for Computing Rational Algebraic K-Theory of Simply Connected Spaces.
A model for the universal space for proper actions of a hyperbolic group.
A Narasimhan-Seshardri-Donaldson Correspondance over Non-orientable Surfaces.
A natural framing of knots.
A natural series for the natural logarithm.
A necessary and sufficient condition for a vector field to be Killing.
A necessary condition for embedding a complex in
A new algorithm for recognizing the unknot.
A new cohomology on special kinds of complex manifolds
A new criterion for knots with free periods
A new geometric invariant associated to the space of flat connections
A new invariant and parametric connected sum of embeddings
We define an isotopy invariant of embeddings of manifolds into Euclidean space. This invariant together with the α-invariant of Haefliger-Wu is complete in the dimension range where the α-invariant could be incomplete. We also define parametric connected sum of certain embeddings (analogous to surgery). This allows us to obtain new completeness results for the α-invariant and the following estimation of isotopy classes of embeddings. In the piecewise-linear category, for a (3n-2m+2)-connected...
A new invariant on hyperbolic Dehn surgery space.
A New Knot Invariant.
A new obstruction to embedding Lagrangian tori.
A new proof of Markov's braid theorem
The purpose of this paper is to introduce a new proof of Markov's braid theorem, in terms of Seifert circles and Reidemeister moves. This means that the proof will be of combinatorial and essentially 2-dimensional nature. One characteristic feature of our approach is that nowhere in the proof will we use or refer to the braid axis. This allows for greater flexibility in various transformations of the diagrams considered. Other proofs of Markov's theorem can be found in [2], [3], [4] and [5].