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We introduce new general techniques for computing the geometric index of a link ▫$L$▫ in the interior of a solid torus ▫$T$▫. These techniques simplify and unify previous ad hoc methods used to compute the geometric index in specific examples and allow a simple computation of geometric index for new ...

For the special linear group ▫${\rm SL}_2({\mathbb C})$▫ and for the singular quadratic Danielewski surface ▫$xy = z^2$▫ we give explicitly a finite number of complete polynomial vector fields that generate the Lie algebra of all polynomial vector fields on them. Moreover, we give three unipotent on ...

We introduce the symplectic density property and the Hamiltonian density property together with the corresponding versions of Andersén-Lempert theory. We establish these properties for the Calogero-Moser space ▫${\cal C}_n$▫ of ▫$n$▫ particles and describe its group of holomorphic symplectic automor ...

We introduce the notion of the algebraic overshear density property which implies both the algebraic notion of flexibility and the holomorphic notion of the density property. We investigate basic consequences of this stronger property, and propose further research directions in this borderland betwe ...