arXiv subjects

Jerome Dubois

Publications and source records attributed to Jerome Dubois.

4 recordsLinked to original sources

arXiv2026

Annihilation of Dirac points and its topological obstruction in a photonic Kagome lattice

Dirac points (DPs) are topological singularities that determine the extraordinary properties of two-dimensional materials. They are generally classified by discrete topological invariants, which determine the possibility of DPs' annihilation upon their collision. Here, we study the behaviors of DPs within a photonic Kagome lattice created in atomic vapor. With optically engineering the potential difference among three sites constituting the Kagome unit cell while preserving time-reversal symmetry and the stability of an isolated DP, the DPs move in reciprocal space. By employing conical diffraction to measure their position and the topological invariant (Euler number), we demonstrate an obstruction to DPs' annihilation during collision and a transition to a case where the Euler number changes and annihilation occurs. Such topological transition is induced by a non-Abelian frame rotation of the eigenstates around the Brillouin zone torus. The associated conversion of the DP quaternionic charges during their motion explains the change of Euler number.

cond-mat.mes-hall↗

arXiv2013

Behavior of the SU(2)-Reidemeister torsion form by mutation

In this paper, we prove that the Reidemeister torsion twisted by the adjoint representation, which is considered as a 1-form, on the SU(2)-character variety of a knot exterior is invariant under mutation along a Conway sphere.

math.GT↗

arXiv2011

Rationality of the SL(2,C)-Reidemeister torsion in dimension 3

If $M$ is a finite volume complete hyperbolic 3-manifold with one cusp and no 2-torsion, the geometric component $X_M$ of its $\SL(2,\BC)$-character variety is an affine complex curve, which is smooth at the discrete faithful representation $ρ_0$. Porti defined a non-abelian Reidemeister torsion in a neighborhood of $ρ_0$ in $X_M$ and observed that it is an analytic map, which is the germ of a unique rational function on $X_M$. In the present paper we prove that (a) the torsion of a representation lies in at most quadratic extension of the invariant trace field of the representation, and (b) the existence of a polynomial relation of the torsion of a representation and the trace of the meridian or the longitude. We postulate that the coefficients of the $1/N^k$-asymptotics of the Parametrized Volume Conjecture for $M$ are elements of the field of rational functions on $X_M$.

math.GT↗

arXiv2009

A volume form on the SU(2)-representation space of knot groups

For a knot K in S^3 we construct according to Casson--or more precisely taking into account Lin and Heusener's further works--a volume form on the SU(2)-representation space of the group of K. We prove that this volume form is a topological knot invariant and explore some of its properties.

math.GT↗