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Applications of quantum invariants in low dimensional topology. (English) Zbl 0892.57005

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.

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
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