23 citations · 33 across the 9 of their papers we have counts for
10 papers · 1 filter
Knots and words
V. Turaev
Knots and links are interpreted as homotopy classes of nanowords and nanophrases in an alphabet consisting of 4 letters. Similar results hold for curves on surfaces. We also discus…
Problems on invariants of knots and 3-manifolds
J. E. Andersen, N. Askitas, D. Bar-Natan +57
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 ope…
Curves on surfaces, charts, and words
Vladimir Turaev
We give a combinatorial description of closed curves on oriented surfaces in terms of certain permutations, called charts. We describe automorphisms of curves in terms of charts an…
Virtual strings
Vladimir Turaev
A virtual string is a scheme of self-intersections of a closed curve on a surface. We introduce virtual strings and study their geometric properties and homotopy invariants. We als…
Knot theory for self-indexed graphs
Matias Graña, Vladimir Turaev
We introduce and study so-called self-indexed graphs. These are (oriented) finite graphs endowed with a map from the set of edges to the set of vertices. Such graphs naturally aris…
Torsions of 3-manifolds
Vladimir Turaev
We give a brief survey of abelian torsions of 3-manifolds.