Elementary spectral invariants and three-dimensional Reeb dynamics
摘要
We survey various recent results on the existence and properties of periodic orbits of Reeb vector fields in three dimensions. We give an introduction to the "elementary spectral invariants" of contact three-manifolds, and we explain how they can be used to prove some of these results. (The remaining results can be proved using spectral invariants from embedded contact homology, of which the elementary spectral invariants are a simplification.) We then review the "alternative ECH capacities" of symplectic four-manifolds, and explain how these can be modified to define the elementary spectral invariants.
引用
@article{arxiv.2605.12958,
title = {Elementary spectral invariants and three-dimensional Reeb dynamics},
author = {Michael Hutchings},
journal= {arXiv preprint arXiv:2605.12958},
year = {2026}
}
备注
51 pages. This document is a set of lecture notes for a minicourse taught by the author at the CIME school on Symplectic Dynamics and Topology in Cetraro in June 2025