The Relationship between Homology and Topological Manifolds via Homology Transversaltiy
The relative coincidence Nielsen number
We define a relative coincidence Nielsen number for pairs of maps between manifolds, prove a Wecken type theorem for this invariant and give some formulae expressing by the ordinary Nielsen numbers.
The Second Homology Group of the Mapping Class Group of an Orientable Surface.
The Seiberg-Witten invariants and 4-manifolds with essential tori.
The Seiberg-Witten invariants of symplectic four-manifolds
The shape genus of a shape map
The slicing number of a knot.
The smallest arithmetic hyperbolic three-orbi-fold.
The Smith Conjecture in dimension four and equivariant gauge theory.
The space of Lipschitz maps from a compactum to an absolute neighborhood LIP extensor
The Spaces of Closed Convex Sets in Euclidean Spaces with the Fell Topology
Let be the space of all non-empty closed convex sets in Euclidean space ℝ ⁿ endowed with the Fell topology. We prove that for every n > 1 whereas .
The spin refinded Kauffman bracket skein module of S1 x S2 and lens spaces.
The structure of pseudo-holomorphic subvarieties for a degenerate almost complex structure and symplectic form on .
The Stucture of Semitopological Monoids on Compact Connected Manifolds.
The Three Big Theorems of Papakyriakopoulos
The topology of deformation spaces of Kleinian groups.
The topology of the Banach–Mazur compactum
Let J(n) be the hyperspace of all centrally symmetric compact convex bodies , n ≥ 2, for which the ordinary Euclidean unit ball is the ellipsoid of maximal volume contained in A (the John ellipsoid). Let be the complement of the unique O(n)-fixed point in J(n). We prove that: (1) the Banach-Mazur compactum BM(n) is homeomorphic to the orbit space J(n)/O(n) of the natural action of the orthogonal group O(n) on J(n); (2) J(n) is an O(n)-AR; (3) is an Eilenberg-MacLane space ; (4) is noncontractible;...
The twisted products of spheres that have the fixed point property
By a twisted product of Sⁿ we mean a closed, 1-connected 2n-manifold M whose integral cohomology ring is isomorphic to that of Sⁿ × Sⁿ, n ≥ 3. We list all such spaces that have the fixed point property.
The virtual cohomological dimension of the mapping class group of an orientable surface.
The virtual Haken conjecture: Experiments and examples.