The Arnold conjecture, Floer homology and symplectic homology

1994 ◽  
pp. 193-271
Author(s):  
Helmut Hofer ◽  
Eduard Zehnder
Keyword(s):  
Floer Homology ◽  
Symplectic Homology ◽  
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 Rabinowitz Floer homology and symplectic homology

2010 ◽  
Vol 43 (6) ◽  
pp. 957-1015 ◽  
Author(s):  
Kai Cieliebak ◽  
Urs Frauenfelder ◽  
Alexandru Oancea
Keyword(s):  
Floer Homology ◽  
Symplectic Homology ◽  
Rabinowitz Floer Homology

scholarly journals Floer homology and Arnold conjecture

1998 ◽  
Vol 49 (1) ◽  
pp. 1-74 ◽  
Author(s):  
Gang Liu ◽  
Gang Tian
Keyword(s):  
Floer Homology ◽  
Arnold Conjecture

scholarly journals COMBINATORIAL KNOT FLOER HOMOLOGY AND DOUBLE BRANCHED COVERS

2013 ◽  
Vol 22 (06) ◽  
pp. 1350014
Author(s):  
FATEMEH DOUROUDIAN
Keyword(s):  
Floer Homology ◽  
Combinatorial Proof ◽  
Branched Covers ◽  
Knot Floer Homology ◽  
Branched Cover ◽  
Heegaard Diagram

Using a Heegaard diagram for the pullback of a knot K ⊂ S3 in its double branched cover Σ2(K), we give a combinatorial proof for the invariance of the associated knot Floer homology over ℤ.

scholarly journals Knot doubling operators and bordered Heegaard Floer homology

2012 ◽  
Vol 5 (3) ◽  
pp. 651-712 ◽  
Author(s):  
Adam Simon Levine
Keyword(s):  
Floer Homology ◽  
Heegaard Floer Homology ◽  
Heegaard Floer
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