11 citations · 13 across the 6 of their papers we have counts for
7 papers · 1 filter
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…
Shadows, ribbon surfaces, and quantum invariants
Alessio Carrega, Bruno Martelli
Eisermann has shown that the Jones polynomial of a -component ribbon link is divided by the Jones polynomial of the trivial -component link. We improve this th…
Step by step categorification of the Jones polynomial in Kauffman's version
Alessio Carrega
Given any diagram of a link, we define on the cube of Kauffman's states a "2-complex" whose homology is an invariant of the associated framed links, and such that the graded Euler…