2012.08930
Eggbeater dynamics on symplectic surfaces of genus 2 and 3
Arnon Chor
correcthigh confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper establishes (A) powers_k(Σ,σ)=∞ for genus 2 or 3 and (B) an embedding F2→Cone_U(Ham(Σ),d_H) by adapting the egg–beater construction and carrying over the Floer/persistence-module arguments that are genus-independent; the only new work is handling the potential non-injectivity of τ_i in genus 2 via an algebraic lemma, and an alternative incompressible embedding for genus 3. The candidate solution follows the same blueprint: egg–beater shears of strength N, spectral-spread lower bounds for (A), and linear Hofer growth implying a monomorphism into the asymptotic cone for (B). Minor discrepancies are present (e.g., the model loosely speaks of incompressible embeddings for both genera, while the paper uses a bounded non-injectivity lemma for genus 2), but they do not affect correctness.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The manuscript cleanly extends known g≥4 results to genera 2 and 3 by a careful adaptation of the egg–beater framework, introducing an algebraic lemma to control non-injectivity in genus 2 and offering an alternative incompressible embedding in genus 3. The Floer/persistence-module deductions are imported appropriately, and the exposition tracks the necessary dependencies. Minor clarifications (explicit upper bounds for Hofer norms in the cone step; a succinct reminder of the spectral-spread properties used) would further improve readability.