2 citations · 2 across the 3 of their papers we have counts for
8 papers
Dimension filtration on loops
J. Mostovoy, J. M. Pérez-Izquierdo
We show that the graded group associated to the dimension filtration on a loop acquires the structure of a Sabinin algebra after being tensored with a field of characteristic zero.…
On the notion of lower central series for loops
Jacob Mostovoy
The commutator calculus is one of the basic tools in group theory. However, its extension to the non-associative context, based on the usual definition of the lower central series…
Spaces of rational maps and the Stone-Weierstrass Theorem
Jacob Mostovoy
It is shown that Segal's theorem on the spaces of rational maps from CP^1 to CP^n can be extended to the spaces of continuous rational maps from CP^m to CP^n for any m less than or…
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…