Garoufalidis, Stavros Applications of quantum invariants in low dimensional topology. (English) Zbl 0892.57005 Topology 37, No. 1, 219-224 (1998). Summary: In this short note the author gives lower bounds for the Heegaard genus of 3-manifolds using various TQFT in \(2+1\) dimensions. He also studies the large \(k\) limit and the large \(G\) limit of our lower bounds, using a conjecture relating the various combinatorial and physical TQFTs. Assuming this conjecture, it is also proved that the set of colored \(SU(N)\) polynomials of a framed knot in \(S^3\) distinguishes the knot from the unknot. Cited in 3 ReviewsCited in 9 Documents MSC: 57M25 Knots and links in the \(3\)-sphere (MSC2010) 57N10 Topology of general \(3\)-manifolds (MSC2010) 81T99 Quantum field theory; related classical field theories Keywords:colored \(SU(N)\) polynomials of a framed knot in \(S^3\); Heegaard genus of 3-manifolds; TQFT PDFBibTeX XMLCite \textit{S. Garoufalidis}, Topology 37, No. 1, 219--224 (1998; Zbl 0892.57005) Full Text: DOI