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 non-criticality of certain families of affine varieties.
The nonuniqueness of Chekanov polynomials of Legendrian knots.
The Novikov conjecture and low-dimensional topology.
The number of critical points in Morse approximations
The number of independent Vassiliev invariants in the Homfly and Kauffman polynomials.
The ?-orbifold Group of a Link.
The orbits of the Hurwitz action of the braid groups on the standard generators
The Hurwitz action of the n-braid group Bₙ on the n-fold direct product of the m-braid group is studied. We show that the orbit of any n- tuple of the n standard generators of consists of the (n-1)th powers of n+1 elements.
The order of the Hopf bundle on projective Stiefel manifolds
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 ...(p) Cohomology of Some k Stage Postnikov Systems
The parity of the Maslov index and the even cobordism category
We give a formula for the parity of the Maslov index of a triple of Lagrangian subspaces of a skew symmetric bilinear form over ℝ. We define an index two subcategory (the even subcategory) of a 3-dimensional cobordism category. The objects of the category are surfaces equipped with Lagrangian subspaces of their real first homology. This generalizes a result of the first author where surfaces are equipped with Lagrangian subspaces of their rational first homology.
The periodic Floer homology of a Dehn twist.
The Picard group of the Burnside ring.
The Poincaré-Bendixson theorem and arational foliations on the sphere
Foliations on the 2-sphere with a finite number of non-orientable singularities are considered. For this class a Poincaré-Bendixson theorem is established. In particular, the work gives an answer to a problem of H. Rosenberg concerning labyrinths.
The Positvity of the Chern Classes of an Ample Vector Bundle.
The principal prolongation of first order -structures
The author uses the concept of the first principal prolongation of an arbitrary principal filter bundle to develop an alternative procedure for constructing the prolongations of a class of the first-order -structures. The motivation comes from the almost Hermitian structures, which can be defined either as standard first-order structures, or higher-order structures, but if they do not admit a torsion-free connection, the classical constructions fail in general.
The proof of Birman's conjecture on singular braid monoids.
The push-out space of immersed spheres.
The QSF property for groups and spaces.