# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
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.

Content:

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.

##### MSC:
 57M27 Invariants of knots and 3-manifolds 00A07 Problem books