On universal groups and three-manifolds.
On universality of countable and weak products of sigma hereditarily disconnected spaces
Suppose a metrizable separable space Y is sigma hereditarily disconnected, i.e., it is a countable union of hereditarily disconnected subspaces. We prove that the countable power of any subspace X ⊂ Y is not universal for the class ₂ of absolute -sets; moreover, if Y is an absolute -set, then contains no closed topological copy of the Nagata space = W(I,ℙ); if Y is an absolute -set, then contains no closed copy of the Smirnov space σ = W(I,0). On the other hand, the countable power of...
On universality of finite powers of locally path-connected meager spaces
It is shown that for every integer n the (2n+1)th power of any locally path-connected metrizable space of the first Baire category is 𝓐₁[n]-universal, i.e., contains a closed topological copy of each at most n-dimensional metrizable σ-compact space. Also a one-dimensional σ-compact absolute retract X is found such that the power X^{n+1} is 𝓐₁[n]-universal for every n.
On unknotting operations of two-brigde knots.
On unkotting tunnels for knots.
On Vassiliev's knot invariants
On vector bundles whose general sections have all projectively equivalent zero-loci
On vector fields coinduced on a differential space and their Lie product
On Verdier's specialization formula for Chern classes.
On (w) and (ts)-regular stratifications.
On weak homotopy
On Yetter's invariant and an extension of the Dijkgraaf-Witten invariant to categorical groups.
On ω-essential mappings onto manifolds
One codimensional Wecken type theorems.
One fixed point actions on low-dimensional spheres.
One-parameter Fixed Point Theory.
One-parameter submonoids in locally complete differentiable monoids
One-relator groups and proper 3-realizability.
Open 3-manifolds and branched coverings: a quick exposition.
Open 3-manifolds, wild subsets of S3 and branched coverings.
In this paper, a representation of closed 3-manifolds as branched coverings of the 3-sphere, proved in [13], and showing a relationship between open 3-manifolds and wild knots and arcs will be illustrated by examples. It will be shown that there exist a 3-fold simple covering p : S3 --> S3 branched over the remarkable simple closed curve of Fox [4] (a wild knot). Moves are defined such that when applied to a branching set, the corresponding covering manifold remains unchanged, while the branching...