33 citations · 66 across the 30 of their papers we have counts for
8 papers · 1 filter
Round twin groups on few strands
Jacob Mostovoy
We study the space of all configurations of ordered points on the circle such that no three points coincide, and in which one of the points (say, the last one) is fixed.…
A presentation for the planar pure braid group
Jacob Mostovoy
We describe the construction of a minimal presentation for the group of planar pure braids on strands. The generators of this presentation are dual to the gene…
Planar pure braids on six strands
Jacob Mostovoy, Christopher Roque-Márquez
The group of planar (or flat) pure braids on strands, also known as the pure twin group, is the fundamental group of the configuration space of labell…
The pure cactus group is residually nilpotent
Jacob Mostovoy
We show that the pure cactus group is residually nilpotent and exhibit a surjective homomorphism whose kernel is r…
Racks as multiplicative graphs
Jacob Mostovoy
We interpret augmented racks as a certain kind of multiplicative graphs and show that this point of view is natural for defining rack homology. We also define the analogue of the g…
On torsion-free nilpotent loops
J. Mostovoy, J. M. Perez-Izquierdo, I. P. Shestakov
We show that a torsion-free nilpotent loop (that is, a loop nilpotent with respect to the dimension filtration) has a torsion-free nilpotent left multiplication group of, at most,…