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Andersen, J. E.; Askitas, N.; Bar-Natan, D.; Baseilhac, S.; Benedetti, R.; Bigelow, S.; Boileau, M.; Bott, R.; Carter, J. S.; Deloup, F.; Dunfield, N.; Fenn, R.; Ferrand, E.; Garoufalidis, S.; Goussarov, M.; Guadagnini, E.; Habiro, H.; Hansen, S. K.; Harikae, T.; Haviv, A.; Jeong, M. -J.; Jones, V.; Kashaev, R.; Kawahigashi, Y.; Kerler, T.; Kidwell, M.; Kohno, T.; Kricker, A.; Le, T. T. Q.; Lescop, C.; Lin, X. -S.; Masbaum, G.; Massuyeau, G.; Morita, S.; Morton, H. R.; Murakami, H.; Murakami, J.; Nakanishi, Y.; Ohtsuki, T.; Ohyama, Y.; Okamoto, M.; Okuda, N.; Park, C. -Y.; Pilo, L.; Polyak, M.; Przytycki, J.; Roberts, J.; Rourke, C.; Rozansky, L.; Sanderson, B.; Sato, N.; Shinohara, Y.; Stanford, T.; Stoimenow, A.; Takata, T.; Thurston, D.; Turaev, V.; Viro, O.; Willerton, S.; Yokota, Y.

Problems on invariants of knots and 3-manifolds. arXiv:math/0406190

Preprint, arXiv:math/0406190 [math.GT] (2004).
Summary: This is a list of open problems on invariants of knots and 3-manifolds with expositions of their history, background, significance, or importance. This list was made by editing open problems given in problem sessions in the workshop and seminars on ‘Invariants of Knots and 3-Manifolds’ held at Kyoto in 2001.

MSC:

20F36 Braid groups; Artin groups
57M25 Knots and links in the \(3\)-sphere (MSC2010)
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
57R56 Topological quantum field theories (aspects of differential topology)
13B25 Polynomials over commutative rings
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B37 Quantum groups (quantized enveloping algebras) and related deformations
18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
20C08 Hecke algebras and their representations
20G42 Quantum groups (quantized function algebras) and their representations
22E99 Lie groups
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
46L37 Subfactors and their classification
57M05 Fundamental group, presentations, free differential calculus
57M50 General geometric structures on low-dimensional manifolds
57N10 Topology of general \(3\)-manifolds (MSC2010)
57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
81T18 Feynman diagrams
81T45 Topological field theories in quantum mechanics
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