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- JENS LIEBERUM
- 2008

We define the Conway skein module C(M) of ordered based links in a 3-manifold M. This module gives rise to C(M)-valued invariants of usual links in M. We determine a basis of the Z[z]-module C(Σ×[0, 1])/Tor(C(Σ×[0, 1])) where Σ is the real projective plane or a surface with boundary. For cylinders over the Möbius strip or the projective plane we derive… (More)

- Jens Lieberum
- 1997

We prove a refinement of Vogel's statement that the Vassiliev invariants of knots coming from semisimple Lie algebras do not generate all Vassiliev invariants. This refinement takes into account the second grading on the Vassiliev invariants induced by cabling of knots. As an application we get an amelioration of the actually known lower bounds for the… (More)

- Jens Lieberum
- 2002

We determine explicitly a rational even Drinfeld associator Φ in a completion of the universal enveloping algebra of the Lie superalgebra gl(1|1) ⊕3. More generally, we define a new algebra of trivalent diagrams that has a unique even horizontal group-like Drinfeld associator Φ. The associator Φ is mapped to Φ by a weight system. As a related result of… (More)

- JENS LIEBERUM
- 2000

We prove that the LMO-invariant of a 3-manifold of rank one is determined by the Alexander polynomial of the manifold, and conversely, that the Alexander polynomial is determined by the LMO-invariant. Furthermore, we show that the Alexander polynomial of a null-homologous knot in a rational homology 3-sphere can be obtained by composing the weight system of… (More)

- Jens Lieberum
- 1998

We calculate the dimensions of the space of Vassiliev invariants coming from the Homfly polynomial of links, and of the space of Vassiliev invariants coming from the Kauffman polynomial of links. We show that the intersection of these spaces is spanned by the Vassiliev invariants coming from the Jones polynomial and from a polynomial called Υ. We also show… (More)

- Jens Lieberum
- 2001

We study Vassiliev invariants of links in a 3-manifold M by using chord diagrams labeled by elements of the fundamental group of M. We construct universal Vassiliev invariants of links in M , where M = P 2 ×[0, 1] is a cylinder over the real projective plane P 2 , M = Σ × [0, 1] is a cylinder over a surface Σ with boundary, and M = S 1 × S 2. A finite… (More)

We consider vector spaces H n,, and F n,, spanned by the degree-n coefficients in power series forms of the Homfly and Kauff-man polynomials of links with components. Generalizing previously known formulas, we determine the dimensions of the spaces for knots the algebra generated by n H n,1 + F n,1 is a polynomial algebra with dim(H n,1 + F n,1) − 1 = n +… (More)

- JENS LIEBERUM
- 1999

We consider vector spaces H n,ℓ and F n,ℓ spanned by the degree n coefficients of suitable power series forms of the Homfly and Kauffman polynomials of links with ℓ components. The intersection H n,ℓ ∩ F n,ℓ contains two Vassiliev invariants, one coming from the Jones polynomial and the second one belonging to another skein theoretically defined polynomial.… (More)