Uniqueness of Symmetries of Knots.
Uniqueness of the embedding of a 2-complex into a 3-manifold.
Units of the string link monoids
We show that the map obtained by viewing a geometric (i.e. representative) braid as a string link induces an isomorphism of the n-strand braid group onto the group of units of the n-strand string link monoid.
Univalent mappings of the plane into itself
Universal coverings of PL-mainfolds via coloured graphs.
Universal tessellations.
All maps of type (m,n) are covered by a universal map M(m,n) which lies on one of the three simply connected Riemann surfaces; in fact M(m,n) covers all maps of type (r,s) where r|m and s|n. In this paper we construct a tessellation M which is universal for all maps on all surfaces. We also consider the tessellation M(8,3) which covers all triangular maps. This coincides with the well-known Farey tessellation and we find many connections between M(8,3) and M.
Unknotting number and knot diagram.
This note is a continuation of a former paper, where we have discussed the unknotting number of knots with respect to knot diagrams. We will show that for every minimum-crossing knot-diagram among all unknotting-number-one two-bridge knot there exist crossings whose exchange yields the trivial knot, if the third Tait conjecture is true.
Unknotting Number, Genus, and Companion Tori.
Unknotting number one knots are prime.
Unknotting tunnels in hyperbolic 3-manifolds.
Unknotting tunnels in two-bridge knot and link complements.
Unraveling the Tangled Complexity of DNA: Combining Mathematical Modeling and Experimental Biology to Understand Replication, Recombination and Repair
How does DNA, the molecule containing genetic information, change its three-dimensional shape during the complex cellular processes of replication, recombination and repair? This is one of the core questions in molecular biology which cannot be answered without help from mathematical modeling. Basic concepts of topology and geometry can be introduced in undergraduate teaching to help students understand counterintuitive complex structural transformations...
Unsolved problems in virtual knot theory and combinatorial knot theory
This paper is a concise introduction to virtual knot theory, coupled with a list of research problems in this field.