33 citations · 66 across the 30 of their papers we have counts for
34 papers
Finite subset spaces of spheres
Jacob Mostovoy
We find the complete rational homology for the finite subset spaces of a -dimensional sphere. We also determine the integral homology in top degrees and obtain a partial des…
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…
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.…
Pre-crossed modules and rack homology
Jacob Mostovoy
We define a homology theory for pre-crossed modules that specifies to rack homology in the case when the pre-crossed module is freely generated by a rack.
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…
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…