5 papers
Shadows and quantum invariants
Alessio Carrega
This is a PhD thesis about low dimensional topology, in particular knot thory in 3-manifolds also different from the 3-sphere, topological applications of quantum invariants, and T…
9 generators of the skein space of the 3-torus
Alessio Carrega
We show that the skein vector space of the 3-torus is finitely generated. We show that it is generated by 9 elements: the empty set, some simple closed curves representing the non…
The Tait conjecture in g(S^1xS^2)
Alessio Carrega
The Tait conjecture states that alternating reduced diagrams of links in S^3 have the minimal number of crossings. It has been proved in 1987 by M. Thistlethwaite, L. Kauffman and…
A proof of the shadow formula for the SU(2)-Reshetikhin-Turaev-Witten invariant
Alessio Carrega
Turaev's shadow formula calculates the SU(2)-Reshetikhin-Turaev-Witten invariants using shadows, and its expression is somehow similar to a Euler characteristic. We give a short pr…
The Tait conjecture in S^1xS^2
Alessio Carrega
The Tait conjecture states that reduced alternating diagrams of links in S^3 have the minimal number of crossings. It has been proved in 1987 by M. Thistlethwaite, L.H. Kauffman an…