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A preprint claims a full proof of the Arnold–Givental conjecture

Shaoyun Bai, Egor Shelukhin, Yi Wang and Guangbo Xu claim the full Arnold–Givental intersection bound over F₂ for fixed loci of anti-symplectic involutions in closed symplectic manifolds. Their argument combines integral Floer theory, an equivariant PSS map and global Kuranishi-chart techniques.

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Stable ID
math-arnold-givental-conjecture-proof-2026
Revision
math-arnold-givental-conjecture-proof-2026.v1
Field
Mathematics · Symplectic topology and Floer theory
Evidence
Tier 1 · Peer reviewed: No
Record state
Provisional · Provisional claimed proof
Last checked

AI role

The manuscript does not disclose a substantive AI role in the proof or writing.

Record details

Problem or result
The Arnold–Givental lower bound for intersections of a real Lagrangian fixed locus with its Hamiltonian image
Authors
Shaoyun Bai, Egor Shelukhin, Yi Wang and Guangbo Xu
Institutions
MIT; Université de Montréal; Hetao Institute of Mathematics and Interdisciplinary Sciences; Rutgers University
Result date
First-version preprint submitted August 27, 2026

Why it matters

The 1989 conjecture is a central symplectic-rigidity statement. The claimed proof gives the full mod-two intersection bound without the restrictions that limited earlier cases.

Limits

This is a first-version, non-peer-reviewed preprint. Amanda Hirschi separately announced joint work in progress with Noah Porcelli on August 26, but no manuscript was available, so that announcement is context rather than independent verification.

Sources

  1. Primary: Bai, Shelukhin, Wang and Xu, full Arnold–Givental proof claim
  2. Independent context: University of Augsburg programme noting a separate proof announcement

Correction and revision history

  1. 2026-09-01 — Added after primary-source, scope, status, AI-role and limitation review.

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