{"paper":{"title":"On the degenerated Arnold-Givental conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Guangcun Lu","submitted_at":"2008-06-01T15:32:24Z","abstract_excerpt":"We present another view dealing with the Arnold-Givental conjecture on a real symplectic manifold\n  $(M, \\omega, \\tau)$ with nonempty and compact real part $L={\\rm Fix}(\\tau)$. For given $\\Lambda\\in (0, +\\infty]$ and $m\\in\\N\\cup\\{0\\}$ we show the equivalence of the following two claims: (i)\n  $\\sharp(L\\cap\\phi^H_1(L))\\ge m$ for any Hamiltonian function $H\\in C_0^\\infty([0, 1]\\times M)$ with Hofer's norm $\\|H\\|<\\Lambda$; (ii) $\\sharp {\\cal P}(H,\\tau)\\ge m$ for every $H\\in C^\\infty_0(\\R/\\Z\\times M)$ satisfying $H(t,x)=H(-t,\\tau(x))\\;\\forall (t,x)\\in\\mathbb{R}\\times M$ and with Hofer's norm $\\|H\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.0122","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}