33 citations · 66 across the 30 of their papers we have counts for
10 papers · 1 filter
A complete invariant for doodles on a 2-sphere
Jacob Mostovoy
We define a complete invariant for doodles on a 2-sphere which takes values in series of chord diagrams of certain type. The coefficients at the diagrams with chords are finite…
Cactus Doodles
Jacob Mostovoy, Andrea Rincón-Prat
Cactus doodles are combinatorial/geometric objects that are related to cactus groups in the same way as knots are related to braids. We define them in terms of local moves on plane…
Encoding knots by clasp diagrams
Jacob Mostovoy, Michael Polyak
We introduce a new combinatorial method to encode knots and links with applications to knot invariants. Clasp diagrams defined in this paper are combinatorial blueprints for buildi…
Introduction to Vassiliev Knot Invariants
S. Chmutov, S. Duzhin, J. Mostovoy
This book is a detailed introduction to the theory of finite type (Vassiliev) knot invariants, with a stress on its combinatorial aspects. It is intended to serve both as a textboo…
Finite type invariants based on the band-pass and doubled delta moves
James Conant, Jacob Mostovoy, Ted Stanford
We study generalizations of finite-type knot invariants obtained by replacing the crossing change in the Vassiliev skein relation by some other local move, analyzing in detail the…
On Invariants of Morse Knots
Jacob Mostovoy, Theodore Stanford
We define and study Vassiliev invariants for (long) Morse knots. It is shown that there are Vassiliev invariants which can distinguish some topologically equivalent Morse knots. In…