2016/10/15 by Carrega, Alessio
#FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1610.04728
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 Turaev's shadows. There is an introduction and a survey for these topics. The thesis uses skein theory and focues on the connected sum of copies of S1xS2 and on the 3-tours as ambient manifolds. The skein space of the 3-torus is computed. The Tait conjecture and Eisermann's theorem have been extended to the connected sums of copies of S1xS2. The knots and links in S1xS2 whose crossing number is at most 3 are tabulated.