Julien March'e

activity

20222025

collaborators

4 papers

math.GT2025

Signatures in TQFT : Asymptotics and Modularity

Julien Marché, Gregor Masbaum

We study the signature $σ_{g} (\frac{q}{p})$ of $SU_{2}$ -TQFT vector spaces associated to surfaces of genus $g$ , as a function of the defining root of unity $ζ = e^{iπ q / p}$ . We pro…

math.GT2025

Reidemeister torsion of two-bridge knots and signatures of TQFT

Julien Marché, Seokbeom Yoon

We establish an explicit relation between the adjoint Reidemeister torsion of the two-bridge knot $K (p, q)$ at any parabolic representation and the Frobenius algebra governing the s…

math.GT2023

Signatures of TQFTs and trace fields of two-bridge knots

Julien Marché

Let $0 < s < r$ be coprime odd integers. We show that the Frobenius algebras governing the signatures of SO $_{3}$ TQFTs at the root $q = exp (iπ s / r)$ contain (and are often equal to) the…

math.GT2022

Toledo invariants of Topological Quantum Field Theories

Bertrand Deroin, Julien Marché

We prove that the Fibonacci quantum representations $ρ_{g, n} : Mod_{g, n} \to PU (p, q)$ for $(g, n) \in {(0, 4), (0, 5), (1, 2), (1, 3), (2, 1)}$ are holonomy representations of complex…