Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2608.04691

Resonances and string point invertibility for compact rank one symmetric spaces

Kai Cieliebak·Alexandru Oancea·Egor Shelukhin
View original source ↗Read source document ↗Export metadata ↓

Abstract

We calculate the Batalin-Vilkovisky (BV) algebra structure of Rabinowitz loop homology for compact rank one symmetric spaces. As a consequence, we prove that such a space satisfies a natural homological condition called string point invertibility if and only if its Euler characteristic is equal to the characteristic of the coefficient field for loop homology. This implies certain cases of Viterbo's conjecture on a uniform bound on the spectral norm of exact Lagrangian submanifolds in cotangent disk bundles. Furthermore, we prove that whenever a compact rank one symmetric space is string point invertible, the critical levels of its loop homology classes with respect to an arbitrary Riemannian metric satisfy a resonance condition with respect to degrees and a density condition for closed geodesics. This generalizes results of Hingston and Rademacher for spheres to a broader class of compact rank one symmetric spaces.

Explore related subjects

math.SGmath.AT

Keep this discovery

BibTeXRIS

Kai Cieliebak, Alexandru Oancea, Egor Shelukhin. 2026-08-05. Resonances and string point invertibility for compact rank one symmetric spaces. https://arxiv.org/abs/2608.04691

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Extended Future Tube Conjecture for Unipotent Subgroups

Let $\Omega$ be the Lorentz future cone in $\mathbb{R}^{d+1}$ with respect to the Lorentz product and let $T^M$ be the $M$-fold product of the future tube $T=\mathbb{R}^{d+1}+i\Omega$. The Lorentz group $\mathrm{SO}_0(1,d)$ acts diagonally on $T^M$, and its complexification $\mathrm{SO}(1,d)^\mathbb{C}$ acts on $\mathbb{C}^{(d+1)\times M}$. We prove that the domain $G^\mathbb{C}\cdot T^M$ is a Stein manifold for any connected unipotent subgroup $G$ of $\mathrm{SO}_0(1,d)$.

math.SG↗
arXiv2026

The First Correction Term in the Asymptotic Expansion of Bohr--Sommerfeld Lagrangian States

Let $\Lambda$ be a compact Bohr--Sommerfeld Lagrangian submanifold of a compact K\"ahler manifold equipped with a holomorphic prequantum line bundle. We study the asymptotic expansion of the Lagrangian states associated with $\Lambda$. In particular, we compute explicitly the first nontrivial correction term and show that it is expressed in terms of geometric invariants of the ambient K\"ahler manifold and the Lagrangian submanifold, including their scalar curvatures, the second fundamental form, and the mean curvature. As a consequence, we obtain the corresponding second-order asymptotic formula for the $L^2$-norm of the Lagrangian states.

math.SG↗
arXiv2026

Classification of Legendrian doubles and suspensions

We define a construction of Legendrians inside contact manifolds that arise by doubling an exact Lagrangian filling in the page of an open book decomposition. This can be seen as a generalization of a previous construction by Courte and Ekholm to arbitrary open books. These Legendrians, called Legendrian doubles, are shown to admit regular flexible exact Lagrangian fillings, and they are thus classified up to Legendrian isotopy by classical data. Finally, we show that the Legendrian suspension construction, as defined by Arikan and the author in previous work,-this is a Legendrian contained inside a page of an open book that is obtained by using Seidel's suspension of Lefschetz fibrations- is a Legendrian double.

math.SG↗