FLOER THEORY OF ANOSOV FLOWS IN DIMENSION THREE

Kai Cieliebak, Oleg Lazarev, Thomas Massoni, Agustin Moreno

correctmedium confidence

Category: math.DS
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves that OC0|W0(V) misses the unit and establishes non-finite split-generation of the orbit category for 4D Anosov Liouville manifolds, via a Topological Disk Lemma and a detailed chain-level analysis. The candidate solution reaches the same conclusions: (A) OC0 does not hit 1 and has infinite-rank kernel, and (B) no strict subfamily split-generates, giving non-smoothness. Their technical routes differ: the paper uses a foliation-based obstruction and Hochschild functoriality to compare HH(A)→HH(A∪{L}), while the model argues via class-splitting, degree considerations, and a Cardy-type CO∘OC vanishing for objects not in A. Both arguments are mathematically consistent and compatible with the paper’s statements.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The manuscript establishes fundamental structural results for wrapped Fukaya categories arising from Anosov Liouville manifolds, notably the failure of Abouzaid’s criterion in this non-Weinstein setting and maximal non-finite split-generation. The Topological Disk Lemma provides a robust geometric obstruction underpinning the Floer-theoretic analysis. Exposition is careful and mostly self-contained. Minor clarifications (e.g., on Hochschild conventions and connections to alternative proofs via CO∘OC) would further assist readers.