scholarly journals The Arnold conjecture for Clifford symplectic pencils

2013 ◽  
Vol 196 (1) ◽  
pp. 95-112 ◽  
Author(s):  
Viktor L. Ginzburg ◽  
Doris Hein
Keyword(s):  
Arnold Conjecture

scholarly journals ARNOLD CONJECTURE AND GROMOV–WITTEN INVARIANT

Topology ◽  
1999 ◽  
Vol 38 (5) ◽  
pp. 933-1048 ◽  
Author(s):  
Kenji Fukaya ◽  
Kaoru Ono
Keyword(s):  
Witten Invariant ◽  
Arnold Conjecture

scholarly journals The E-Cohomological Conley Index, Cup-Lengths and the Arnold Conjecture on T 2n

2019 ◽  
Vol 19 (3) ◽  
pp. 519-528 ◽  
Author(s):  
Maciej Starostka ◽  
Nils Waterstraat
Keyword(s):  
Lower Bound ◽  
Hilbert Spaces ◽  
Critical Points ◽  
Short Proof ◽  
Conley Index ◽  
Module Structure ◽  
Arnold Conjecture ◽  
Natural Module ◽  
The Way

Abstract We show that the E-cohomological Conley index, that was introduced by the first author recently, has a natural module structure. This yields a new cup-length and a lower bound for the number of critical points of functionals on Hilbert spaces. When applied to the setting of the Arnold conjecture, this paves the way to a short proof on tori, where it was first shown by C. Conley and E. Zehnder in 1983.

scholarly journals On variants of Arnold conjecture

2020 ◽  
pp. 277-286
Author(s):  
Roman Golovko
Keyword(s):  
Arnold Conjecture

The arnold conjecture

2017 ◽  
Author(s):  
Dusa McDuff ◽  
Dietmar Salamon
Keyword(s):  
Fixed Points ◽  
Generating Functions ◽  
Floer Homology ◽  
Lagrangian Submanifolds ◽  
Index Theory ◽  
Intersection Problem ◽  
Arnold Conjecture ◽  
Conley Index Theory ◽  
Cotangent Bundles ◽  
Symplectic Action

This chapter contains a proof of the Arnold conjecture for the standard torus, which is based on the discrete symplectic action. The symplectic part of this proof is very easy. However, for completeness of the exposition, one section is devoted to a fairly detailed discussion of the relevant Conley index theory and of Ljusternik–Schnirelmann theory. Closely related to the problem of finding symplectic fixed points is the Lagrangian intersection problem. The chapter outlines a proof of Arnold’s conjecture for cotangent bundles that again uses the discrete symplectic action, this time to construct generating functions for Lagrangian submanifolds. The chapter ends with a brief outline of the construction and applications of Floer homology.

scholarly journals Givental’s Non-linear Maslov Index on Lens Spaces

2020 ◽  
Author(s):  
Gustavo Granja ◽  
Yael Karshon ◽  
Milena Pabiniak ◽  
Sheila Sandon
Keyword(s):  
Projective Space ◽  
Maslov Index ◽  
Universal Cover ◽  
Lens Spaces ◽  
Real Projective Space ◽  
Arnold Conjecture ◽  
Identity Component ◽  
Contact Rigidity ◽  
Non Linear

Abstract Givental’s non-linear Maslov index, constructed in 1990, is a quasimorphism on the universal cover of the identity component of the contactomorphism group of real projective space. This invariant was used by several authors to prove contact rigidity phenomena such as orderability, unboundedness of the discriminant and oscillation metrics, and a contact geometric version of the Arnold conjecture. In this article, we give an analogue for lens spaces of Givental’s construction and its applications.

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