Wyniki wyszukiwania

1

The equation [B,(A-1)(A,B)] = 0 and virtual knots and links

100%

Budden S., Fenn R.

Fundamenta Mathematicae

|

2004

|

tom 184

|

nr 1

19-29

EN

Let A, B be invertible, non-commuting elements of a ring R. Suppose that A-1 is also invertible and that the equation [B,(A-1)(A,B)] = 0 called the fundamental equation is satisfied. Then this defines a representation of the algebra ℱ = A, B | [B,(A-1)(A,B)] = 0. An invariant R-module can then be defined for any diagram of a (virtual) knot or link. This halves the number of previously known relations and allows us to give a complete solution in the case when R is the quaternions.

2

Virtual knot theory-unsolved problems

81%

Fenn R., Kauffman L., Manturov V.

Fundamenta Mathematicae

|

2005

|

tom 188

|

nr 1

293-323

EN

The present paper gives a quick survey of virtual and classical knot theory and presents a list of unsolved problems about virtual knots and links. These are all problems in low-dimensional topology with a special emphasis on virtual knots. In particular, we touch new approaches to knot invariants such as biquandles and Khovanov homology theory. Connections to other geometrical and combinatorial aspects are also discussed.

3

Unsolved problems in virtual knot theory and combinatorial knot theory

81%

Fenn R., Ilyutko D., Kauffman L., Manturov V.

Banach Center Publications

|

2014

|

tom 103

|

nr 1

9-61

EN

This paper is a concise introduction to virtual knot theory, coupled with a list of research problems in this field.

Ograniczanie wyników

2 Fundamenta Mathematicae

1 Banach Center Publications

3 Fenn R.

2 Kauffman L.

2 Manturov V.

1 Budden S.

1 Ilyutko D.

1 2014

1 2005

1 2004

The equation [B,(A-1)(A,B)] = 0 and virtual knots and links

Virtual knot theory-unsolved problems

Unsolved problems in virtual knot theory and combinatorial knot theory