The volume spectrum of hyperbolic 4-manifolds.
The Wecken property of the projective plane
A proof is given of the fact that the real projective plane has the Wecken property, i.e. for every selfmap , the minimum number of fixed points among all selfmaps homotopic to f is equal to the Nielsen number N(f) of f.
The Whitehead link, the Borromean rings and the knot 946 are universal.
A link L in S3 is universal if every closed, orientable 3-manifold is a covering of S3 branched over L. Thurston [1] proved that universal links exist and he asked if there is a universal knot, and also if the Whitehead link and the Figure-eight knot are universal. In [2], [3] we answered the first question by constructing a universal knot. The purpose of this paper is to prove that the Whitehead link and the Borromean rings, among others, are universal. The question about the Figure-eight knot...
The Yang-Mills equations and the topology of 4-manifolds
Theorem on the union of two topologically flat cells of codimension 1 in .
Thin presentation of knots and lens spaces.
Three-Dimensional Poincaré Duality Groups Which Are Extensions.
Three-manifolds and the Temperley-Lieb algebra.
Three-manifolds having complexity at most 9.
Tight Polyhedral Klein Bottles, Projective Planes, and Möbius Bands.
Tight Topological Embeddings of the Real Projective Plane in E5.
Tightness and efficiency of irreducible automorphisms of handlebodies.
Topological Classification of 4-Dimensional Complete Intersections.
Topological classification of closed convex sets in Fréchet spaces
We prove that each non-separable completely metrizable convex subset of a Fréchet space is homeomorphic to a Hilbert space. This resolves a more than 30 years old problem of infinite-dimensional topology. Combined with the topological classification of separable convex sets due to Klee, Dobrowolski and Toruńczyk, this result implies that each closed convex subset of a Fréchet space is homeomorphic to for some cardinals 0 ≤ n ≤ ω, 0 ≤ m ≤ 1 and κ ≥ 0.
Topological classification of multiaxial -actions (with an appendix by Jared Bass)
This paper begins the classification of topological actions on manifolds by compact, connected, Lie groups beyond the circle group. It treats multiaxial topological actions of unitary and symplectic groups without the dimension restrictions used in earlier works by M. Davis and W. C. Hsiang on differentiable actions. The general results are applied to give detailed calculations for topological actions homotopically modeled on standard multiaxial representation spheres. In the present topological...
Topological classification of strong duals to nuclear (LF)-spaces
We show that the strong dual X’ to an infinite-dimensional nuclear (LF)-space is homeomorphic to one of the spaces: , , , , or , where and . In particular, the Schwartz space D’ of distributions is homeomorphic to . As a by-product of the proof we deduce that each infinite-dimensional locally convex space which is a direct limit of metrizable compacta is homeomorphic either to or to . In particular, the strong dual to any metrizable infinite-dimensional Montel space is homeomorphic either...
Topological components of spaces of representations.
Topological groups and convex sets homeomorphic to non-separable Hilbert spaces
Let X be a topological group or a convex set in a linear metric space. We prove that X is homeomorphic to (a manifold modeled on) an infinite-dimensional Hilbert space if and only if X is a completely metrizable absolute (neighborhood) retract with ω-LFAP, the countable locally finite approximation property. The latter means that for any open cover of X there is a sequence of maps (f n: X → X)nεgw such that each f n is -near to the identity map of X and the family f n(X)n∈ω is locally finite...
Topological manifolds and real algebraic geometry
We study the problem of approximating, up to homotopy, compact topological manifolds by real algebraic varieties. As a consequence, we realize any integral non-degenerate quadratic form as the intersection form of a real algebraic variety. This is related to a well-known result, due to Freedman [F], on the topology of closed simply-connected topological -manifolds.
Topological Order Complexes and Resolutions of Discriminant Sets