arXiv subjects

Stefano Iovieno

Publications and source records attributed to Stefano Iovieno.

3 recordsLinked to original sources

arXiv2022

A computational study of the number of connected components of positive Thompson links

Almost a decade ago Vaughan Jones introduced a method to produce knots from elements of the Thompson groups $F$, which was later extended to the Brown-Thompson group $F_3$. In this article we define a way to produce permutations out of elements of the $F$ and $F_3$ that we call Thompson permutations. The number of orbits of each Thompson permutation coincides with the number of connected components of the link. We explore the positive elements of $F_3$ of fixed \emph{width} and \emph{height} and make some conjectures based on numerical experiments. In order to define the Thompson permutations we need to assign an orientation to each link produced from elements of $F$ and $F_3$. We prove that all oriented links can be produced in this way.

math.GT↗

arXiv2020

Positive energy representations of Sobolev diffeomorphism groups of the circle

We show that any positive energy projective unitary representation of Diff(S^1) extends to a strongly continuous projective unitary representation of the fractional Sobolev diffeomorphisms D^s(S^1) for any real s>3, and in particular to C^k-diffeomorphisms Diff^k(S^1) with k>=4. A similar result holds for the universal covering groups provided that the representation is assumed to be a direct sum of irreducibles. As an application we show that a conformal net of von Neumann algebras on S^1 is covariant with respect to D^s(S^1), s > 3. Moreover every direct sum of irreducible representations of a conformal net is also D^s(S^1)-covariant.

math.RT↗

arXiv2018

Solitons and nonsmooth diffeomorphisms in conformal nets

We show that any solitonic representation of a conformal (diffeomorphism covariant) net on S^1 has positive energy and construct an uncountable family of mutually inequivalent solitonic representations of any conformal net, using nonsmooth diffeomorphisms. On the loop group nets, we show that these representations induce representations of the subgroup of loops compactly supported in S^1 \ {-1} which do not extend to the whole loop group. In the case of the U(1)-current net, we extend the diffeomorphism covariance to the Sobolev diffeomorphisms D^s(S^1), s > 2, and show that the positive-energy vacuum representations of Diff_+(S^1) with integer central charges extend to D^s(S^1). The solitonic representations constructed above for the U(1)-current net and for Virasoro nets with integral central charge are continuously covariant with respect to the stabilizer subgroup of Diff_+(S^1) of -1 of the circle.

math-ph↗