Tootfinder

Higher path groupoids and the holonomy of formal power series connections
Matthew Cellot
https://arxiv.org/abs/2506.23880 https://arx…

Higher path groupoids and the holonomy of formal power series connections
Building on ideas of Kohno, we develop a framework for the construction of higher holonomy functors via the transport of formal power series connections. Using these techniques, we obtain functors from the path groupoid, the path 2-groupoid, and the path 3-groupoid of a manifold. As an application, we construct a Gray functor from the path 3-groupoid of the configuration space of $m$ points in $\mathbb{R}^n$ for $n\geqslant 4$.

Categorified structures over moduli spaces: Anomalies, non-invertible symmetries, and exceptional holonomy
A. Perez-Lona, E. Sharpe, X. Yu
https://arxiv.org/abs/2506.19909

Categorified structures over moduli spaces: Anomalies, non-invertible symmetries, and exceptional holonomy
In this note, we propose an extension of the relation between worldsheet global symmetries and structures over moduli spaces of superconformal field theories (SCFTs) to include noninvertible symmetries. The most familiar examples of such structures associated to an ordinary symmetry are the Bagger-Witten line bundles, which arise over the moduli spaces of two-dimensional N=(2,2) SCFTs from a non-anomalous worldsheet U(1)_R symmetry and its associated spectral flow operators. Generalizing this s…

Left-invariant ${\rm G}_2^*$-structures of type III
Viviana del Barco, Ana Cristina Ferreira, Ines Kath
https://arxiv.org/abs/2506.14031 https://

Left-invariant ${\rm G}_2^*$-structures of type III
We investigate left-invariant ${\rm G}_2^*$-structures on 7-dimensional Lie groups, focusing on those whose holonomy algebras are indecomposable and of type III, the latter meaning that the socle of the holonomy representation is maximal. Building on the classification of indecomposable holonomy algebras contained in $\mathfrak g_2^*$, we determine which ones arise as infinitesimal holonomy algebras of type III for left-invariant ${\rm G}_2^*$-structures. Our main result shows that only abelian…

This https://arxiv.org/abs/2410.22275 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Piecewise geodesic Jordan curves II: Loewner energy, projective structures, and accessory parameters
In this paper we consider Jordan curves on the Riemann sphere passing through $n \ge 3$ given points. We show that in each relative isotopy class of such curves, there exists a unique curve that minimizes the Loewner energy. These curves have the property that each arc between two consecutive points is a hyperbolic geodesic in the domain bounded by the other arcs. This geodesic property lets us define a complex projective structure whose holonomy lies in $\mathrm{PSL}(2,\mathbb{R})$. We show th…

Normal Holonomy of Complex Hyperbolic Submanifolds
Santiago Casta\~neda Montoya, Carlos E. Olmos
https://arxiv.org/abs/2506.11323 https://

Normal Holonomy of Complex Hyperbolic Submanifolds
We prove that the restricted normal holonomy group of a Kähler submanifold of the complex hyperbolic space $\mathbb{C}H^{n}$ is always transitive, provided the index of relative nullity is zero. This contrasts with the case of $\mathbb{C}P^{n}$, where a Berger type result was proved by Console, Di Scala, and the second author. The proof is based on lifting the submanifold to the pseudo-Riemannian space $\mathbb{C}^{n,1}$ and developing new tools to handle the difficulties arising from possible…

This https://arxiv.org/abs/2210.14765 has been replaced.
link: https://scholar.google.com/scholar?q=a

Holed cone structures on 3-manifolds
We introduce holed cone structures on 3-manifolds to generalize cone structures. In the same way as a cone structure, a holed cone structure induces the holonomy representation. We consider the deformation space consisting of the holed cone structures on a 3-manifold whose holonomy representations are irreducible. This deformation space for positive cone angles is a covering space on a reasonable subspace of the character variety.

Anomaly freedom in effective Loop Quantum Cosmology refined: extended functional dependence of the counter-terms
Maxime De Sousa, Aur\'elien Barrau, Killian Martineau
https://arxiv.org/abs/2506.14308

Anomaly freedom in effective Loop Quantum Cosmology refined: extended functional dependence of the counter-terms
Instead of assuming that they depend only on the background variables, we investigate the hypothesis that counter-terms appearing in the deformed algebra approach to loop quantum cosmology depend on the full phase-space variables. We derive the associated anomalies and solve the entire system in several specific cases. New restrictions on the generalized holonomy corrections are obtained.

Thin homotopy and the signature of piecewise linear surfaces
Francis Bischoff, Darrick Lee
https://arxiv.org/abs/2506.16657 https://a…

Thin homotopy and the signature of piecewise linear surfaces
We introduce a crossed module of piecewise linear surfaces and study the signature homomorphism, defined as the surface holonomy of a universal translation invariant $2$-connection. This provides a transform whereby surfaces are represented by formal series of tensors. Our main result is that the signature uniquely characterizes a surface up to translation and thin homotopy, also known as tree-like equivalence in the case of paths. This generalizes a result of Chen and positively answers a ques…

This https://arxiv.org/abs/2408.01169 has been replaced.
initial toot: https://mastoxiv.page/@a…

Spin parallel transport and holonomy on a spherical two-dimensional electron gas
The quantum conductance of circuits built on flat (Euclidean) two-dimensional electron gases in known to show a symmetric response to the inversion of Rashba spin-orbit coupling fields in Aharonov-Casher interference patterns. Here, we show that this symmetry breaks down in curved (non-Euclidean) circuits defined on a spherical two-dimensional electron gas. We demonstrate that this is a consequence of parallel spin transport and holonomy on the surface of the sphere, and that a symmetric respon…

This https://arxiv.org/abs/2410.20529 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Formation of nonsingular spherical black holes with holonomy corrections
We present a canonical model of spherical gravity with covariant corrections motivated by loop quantum gravity. The effective Hamiltonian defines univocally a family of geometries that generalizes the Lemaître-Tolman-Bondi spacetimes, and they can be matched to the vacuum of the theory across a timelike hypersurface comoving with the flow of matter. Such is precisely the complete spacetime picture of a spherical star subject to its own gravitational pull. The singularity gets replaced with a s…

This https://arxiv.org/abs/2311.07459 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On homogeneous plane waves
Plane waves are a special class of Lorentzian spaces with a parallel null vector field. They are of great importance in Geometry (e.g. Lorentzian holonomy) and in Physics (General Relativity as well as alternative gravity theories). Our contribution in the present paper aims at a rigorous mathematical treatment focusing on completeness of Killing fields, and globality of coordinates. Equivalence of different approaches to plane waves is by no means easy to handle. We use here cohomogeneity one …