Tootfinder

Virtual fibring of Poincar\'e-duality groups
Sam P. Fisher, Giovanni Italiano, Dawid Kielak
https://arxiv.org/abs/2506.14666 https://

Virtual fibring of Poincaré-duality groups
We show that a RFRS Poincaré-duality group $G$ admits a virtual epimorphism to the integers whose kernel is itself a Poincaré-duality group over every field if and only if the $L^2$-homology of $G$ vanishes and so do the positive-characteristic variants thereof. Our investigations yield a more general relationship between cohomology at infinity of groups that algebraically fibre and their fibres. In particular, we show that if the fundamental group of an aspherical manifold of dimension at …

On the notion of elementary particles on curved space-times
Alberto Ibort, Arnau Mas, Luca Schiavone
https://arxiv.org/abs/2506.14296 https://

On the notion of elementary particles on curved space-times
Wigner's program that identified elementary particles with unitary irreducible representations of Poincaré group, is extended, inspired by the modern categorical/groupoidal picture of Quantum Mechanics, to general Lorentzian space-times.

The building blocks of asymptotically flat spacetimes
Shadi Ali Ahmad
https://arxiv.org/abs/2506.11190 https://arxiv.org/pdf/2506.111…

The building blocks of asymptotically flat spacetimes
The classification of all possible induced representations arising from theories admitting a Poincaré symmetry has molded our very conception of particles in flat space. In this note, we argue that if one takes the same viewpoint on the asymptotic symmetry group instead of the global one, the familiar relativistic classification is enhanced to provide a new notion of excitations in asymptotically flat spacetimes. These excitations blur the line between the quantum description of a particle and…

The numerical Amitsur group
Alexander Duncan, Shreya Sharma
https://arxiv.org/abs/2505.23957 https://arxiv.org/pdf/2505.23957

The numerical Amitsur group
The Amitsur subgroup of a variety with a group action measures the failure of the action to lift to the total spaces of its line bundles. We introduce the "numerical Amitsur group," which is an approximation of the ordinary Amitsur subgroup that can be computed using only the Euler-Poincaré characteristic on the Picard group. As an application, we find a uniform upper bound on the exponent of the Amitsur subgroup that depends only on the dimension and arithmetic genus of the variety and is ind…

This https://arxiv.org/abs/2505.20459 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Holographic Timelike c-function
The integration of high-energy degrees of freedom along the renormalization group (RG) flow in Poincaré-invariant theories can be captured by a monotonic c-function. For such theories, holographic monotonic c-functions have been constructed using entanglement entropy. However, in theories with broken Lorentz invariance, such constructions generally fail, reflecting both the violation of the entanglement RG monotonicity and its limitations in capturing certain properties of non-relativistic RG …