2 citations · 3 across the 7 of their papers we have counts for
7 papers
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 a new and elementary proof of the following fact:…
Sharpness of the Morton-Franks-Williams inequality for positive knots and links
Ilya Alekseev
We provide a combinatorial characterisation of positive diagrams satisfying the equality in the Morton-Franks-Williams bound for the degrees of the HOMFLY-PT polynomial. This chara…
Action of automorphisms of pure braid groups on homotopy groups of two-sphere
Ilya Alekseev, Vasily Ionin, Mikhail Mikhailov
We examine the Moore complex of the Delta-group structure related to the pure braid groups and introduced by Berrick, Cohen, Wong, and Wu. We prove that the cycle and the boundary…
New classes of minimal knot diagrams
Ilya Alekseev
We describe a new class of minimal link diagrams. This class includes certain alternating diagrams, the standard diagrams of all torus links, and numerous homogeneous diagrams whos…
The language of geodesics for the discrete Heisenberg group
Ilya Alekseev, Ruslan Magdiev
In this paper, we give a complete description of the language of geodesic words for the discrete Heisenberg group with respect to the standard two-element generatin…
On minimal crossing number braid diagrams and homogeneous braids
Ilya Alekseev, Geidar Mamedov
We study braid diagrams with a minimal number of crossings. Such braid diagrams correspond to geodesic words for the braid groups with standard Artin generators. We prove that a di…
Higher Jacobi identities
Ilya Alekseev, Sergei O. Ivanov
By definition the identities and hold in any Lie algebra. It is easy to check that the identity $[x_1,x_2,x_3,…