THE ARNOLD CONJECTURE FOR SINGULAR SYMPLECTIC MANIFOLDS

The paper proves Theorem A (for b^{2m}-symplectic manifolds with acyclic graph) and Theorem B (surface case) by desingularization and a capping/extension argument, not by computing a Floer homology; these statements and their hypotheses are explicit in the PDF (Theorem A/B) and the acyclicity mechanism via desingularization is described in the introduction and Section 4 . The authors also establish a maximum principle (Theorem C) and define a Floer-type complex, but they explicitly state that invariance of this homology (and a computation in topological terms) is beyond the scope of the present paper (Remark 5.5) . By contrast, the model’s argument hinges on unproven steps: a continuation/invariance principle for the bm-Floer homology and an identification HF^*(H) ≅ ⊕_i H^*(M_i, ∂M_i; Z2), which the paper leaves as an open direction, not an established result. Moreover, the model’s surface computation is internally inconsistent: it first identifies HF on each component with relative cohomology (which would give rank 2g_i + b_i) but then asserts the different bound max{2 + 2g_i − b_i, 0}—the latter is the paper’s combinatorial lower bound (Theorem 4.13) rather than a Floer homology rank computation . Hence the paper’s results are correct as stated, while the model’s proof relies on claims not supported (or contradicted) by the paper.