A combinatorial formula for the signature of alternating diagrams
We express the signature of an alternating link in terms of some combinatorial characteristics of its diagram.
A combinatorial theorem for a symmetric triangulation of the sphere
A common fixed point theorem for commuting expanding maps on nilmanifolds.
A comparison principle and extension of equivariant maps.
A comparison theorem for -homology
A compendium of pseudoholomorphic beasts in .
A complement to the theory of equivariant finiteness obstructions
It is known ([1], [2]) that a construction of equivariant finiteness obstructions leads to a family of elements of the groups . We prove that every family of elements of the groups can be realized as the family of equivariant finiteness obstructions of an appropriate finitely dominated G-complex X. As an application of this result we show the natural equivalence of the geometric construction of equivariant finiteness obstruction ([5], [6]) and equivariant generalization of Wall’s obstruction...
A complete description of normal surfaces for infinite series of 3-manifolds.
A computation in Khovanov-Rozansky homology
We investigate the Khovanov-Rozansky invariant of a certain tangle and its compositions. Surprisingly the complexes we encounter reduce to ones that are very simple. Furthermore, we discuss a "local" algorithm for computing Khovanov-Rozansky homology and compare our results with those for the "foam" version of sl₃-homology.
A computation of the Kontsevich integral of torus knots.
A Concordance Classification of p. 1. Homeomorphisms of Real Projective Space.
A conjecture concerning positive Ricci curvature and the Witten genus.
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 Converse to the P.A. Smith Theorem for Nonunitary Homology Spheres.
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"