6 citations · 9 across the 9 of their papers we have counts for
7 papers · 1 filter
Affine transverse foliations in sphere bundles
Ilya Alekseev, Ivan Nasonov, Gaiane Panina
Let~ be an oriented sphere bundle supporting a smooth affine transverse foliation. We give an upper bound for the Euler number of the bundle.…
Squared Distance Function on the Configuration Space of a planar Spider with Applications to Hooke Energy and Voronoi Distance
Maciej Denkowski, Gaiane Panina, Dirk Siersma
Spider mechanisms are the simplest examples of arachnoid mechanisms, they are one step more complicated than polygonal linkages. Their configuration spaces have been studied intens…
Compactifications of associated with Alexander self-dual complexes: Chow ring, -classes and intersection numbers
Ilia Nekrasov, Gaiane Panina
An Alexander self-dual complex gives rise to a compactification of , called ASD compactification, which is a smooth algebraic variety. ASD compactifications include (but a…
Geometric presentation for the cohomology ring of polygon spaces
Ilia Nekrasov, Gaiane Panina
We describe the cohomology ring of the moduli space of a flexible polygon in geometrically meaningful terms. We propose two presentations, both are computation friendly: there are…
Diagonal complexes for surfaces of finite type and surfaces with involution
Joseph Gordon, Gaiane Panina
Two related constructions are studied: (1) The diagonal complex and its barycentric subdivision related to a \textit{punctured} oriented surface eq…
Polygons with prescribed edge slopes: configuration space and extremal points of perimeter
Joseph Gordon, Gaiane Panina, Yana Teplitskaya
We describe the configuration space of polygons with prescribed edge slopes, and study the perimeter as a Morse function on . We characterize…