Problems on invariants of knots and 3-manifolds

By J. Andersen, N. Askitas, Dror Bar-Natan, S. Baseilhac, R. Benedetti, Stephen Bigelow, M. Boileau, R. Bott, J. Scott Carter, F. Deloup and 50 more. 2004

128 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1c402fb91afc62748aca30fcb4a10a2e0ffe0151

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Citations in the corpus

Cyclotomic Completions of Polynomial Rings (2002, methodology): “The ring Z[q] is used in the definition of the new invariant I(M) of an integral homology 3-sphere M that we announced in [1] (where Z[q] is denoted by Ẑ[q]), see also [11].”
A Survey of Classical Knot Concordance (2003, methodology): “A related invariant that is more closely tied to concordance was introduced by Askitas [4, 93], which we call the slicing number of a knot: u s (K) is the minimum number of crossing changes required to convert a knot into a slice knot.”
Cocycle knot invariants from quandle modules and generalized quandle homology (2003, methodology): “us the second item in Example 2.1 occurs in semi-direct product of groups, when θ = 0 and hence κ = 0. Note also that the second case of Lemma 3.1 agrees with the quandle action considered by Ohtsuki [35]. Example 3.2 The wreath product of groups gives speciﬁc examples as follows. Let N = (Zq)n for ”
Matrices and finite biquandles (2006, methodology): “A list of known connected quandles together with an algorithm for finding connected quandles is given in [ 9 ].”
Matrices and Finite Quandles (2004, background): “4 6 Connected quandles are of prime interest since knot quandles are connected. A list of known connected quandles together with an algorithm for ﬁnding connected quandles is given in [9]. A previous computer search by S. Yamada for isomorphism classes of quandles is mentioned, though only t”