A New Point of View in the Theory of Knot and Link Invariants

Details A New Point of View in the Theory of Knot and Link Invariants A New Point of View in the Theory of Knot and Link Invariants

2001-04-18

arxiv.org/abs/math/0104180v4

Mathematics

Quantum Algebra

25 pages, some minor corrections made, version to appear in Jorunal of Knot Theory and its Ramifications

Scientific paper

Recent progress in string theory has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be understood in topological terms. We describe in detail how to construct the new polynomials and we conjecture their general structure. This leads to new conjectures on the algebraic structure of the quantum-group polynomial invariants. We also describe the geometrical meaning of the coefficients in terms of the enumerative geometry of Riemann surfaces with boundaries in a certain Calabi-Yau threefold.

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