Description

• Title:
  On the degenerate Arnold conjecture on T^{2m} x CP^n
• Creator:
  Asselle, Luca;
  Starostka, Maciej
• Description:
  In the 1960s Arnold conjectured that a Hamiltonian diffeomorphism of a closed connected symplectic manifold $(M,\omega)$ should have at least as many contractible fixed points as a smooth function on $M$ has critical points. Such a conjecture can be seen as a natural generalization of Poincaré's last geometric theorem and represents one of the most famous problems in symplectic geometry — still open today in its full generality. In this paper, we build on a recent approach of the authors and Izydorek to the Arnold conjecture on $\mathbb C\mathbb P^n$ to show that the (degenerate) Arnold conjecture holds for Hamiltonian diffeomorphisms $\phi$ of $\T^{2m}\times \mathbb C\mathbb P^n$, $m,n\geq 1$, which are $C^0$-close to the identity in the $\mathbb C \mathbb P^n$-direction, namely that any such $\phi$ has at least $\text{CL}\big(\T^{2m}\times \mathbb C\mathbb P^n\big)+1= 2m+n+1$ contractible fixed points.
• Object availability:
  free access
• Date:
  2025.06.14
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Online First Articles; 1 - 16;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/62315/42831 ;https://apcz.umk.pl/TMNA/article/view/62315/42832
• Subject:
  Arnold conjecture;
  Conley index;
  Primary: 58E05 37J12;
  Secondary: 37B30
• Identifier: https://apcz.umk.pl/TMNA/article/view/62315
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other