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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…
Lattices in R^2 and finite subsets of a circle
Jacob Mostovoy
An elementary geometric construction is used to relate the space of lattices in a plane to the space exp_3(S^1) of the subsets of a circle of cardinality at most 3. As a consequenc…
Free groups and finite type invariants of pure braids
Jacob Mostovoy, Simon Willerton
Finite type invariants (also known as Vassiliev invariants) of pure braids are considered from a group-theoretic point of view. New results include a construction of a universal in…
On a Map From Pure Braids to Knots
Jacob Mostovoy, Theodore Stanford
We study a certain type of braid closure which resembles the plat closure but has certain advantages; for example, it maps pure braids to knots. The main results of this note are a…