An invitation to knot theory: virtual and classical
0
Type: Book
"61" Result
Sort By:
From prehistory to the present, knots have been used for purposes both artistic and practical. The modern science of Knot Theory has ramifications for biochemistry and mathematical physics and is a rich source of research projects for undergraduate and graduate students and prof…
Quandles and their kin--kei racks, biquandles, and biracks--are algebraic structures whose axioms encode the movement of knots in space, say Elhamdadi and Nelson, in the same way that groups encode symmetry and orthogonal transformations encode rigid motion. They introduce quand…
A knot K is said to have Property P if simply-connected 3-manifolds cannot be obtained by non-trivial Dehn surgeries along K. Torus knots, twist knots, a class of 2-bridge knots, and 2-bridge knots with 9 or fewer crossings are known to have Property P. On the other hand, Ochiai…
We investigate higher-order cohomology operations (Massey products) on complements of links of circles in [italic]S³. These are known to be essentially equivalent to the [lowercase Greek]Mu [with macron]-invariants of John Milnor, which detect whether or not the longitudes of th…
There are three chapters to the memoir. The first defines and develops the notion of the index of a graph. The next chapter presents the general application of the graph index to knot theory. The last section is devoted to particular examples, such as determining the braid index…
Topological invariants of quasi-ordinary singularities: This paper deals with topological invariants of quasi-ordinary singularities on hypersurfaces. Embedded topological classification of quasi-ordinary singularities: The author generalizes the known embedded topological clas…
"The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathema…
"The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathema…
