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Problems on invariants of knots and 3-manifolds. (English) Zbl 1163.57302
Ohtsuki, T. (ed.) et al., Invariants of knots and 3-manifolds. Proceedings of the workshop, Kyoto, Japan, September 17–21, 2001. Coventry: Geometry and Topology Publications. Geom. Topol. Monogr. 4, 377-572 (2002).

From the text: 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.


1. Polynomial invariants of knots; 2. Finite type invariants of knots; 3. The Kontsevich invariant; 4. Skein modules; 5. Quandles; 6. Braid group representations; 7. Quantum and perturbative invariants of 3-manifolds; 8. Topological quantum field theory; 9. The state-sum invariants of 3-manifolds derived from 6j-symbols; 10. Casson invariant and finite type invariants of 3-manifolds; 11. The LMO invariant; 12. Other problems (Legendrian knots, knots and finite groups, the numbers of colorings and some local moves, knotted trivalent graphs, quantum groups etc).

An electronic version of the list, together with recent updates, is available at http://www.kurims.kyoto-u.ac.jp/~tomotada/proj01.

57M27Invariants of knots and 3-manifolds
00A07Problem books