The Arnold-Givental conjecture and moment Floer homology

By Urs Frauenfelder. 2003

118 citations recorded by the source corpus.

We prove the Arnold-Givental conjecture for a class of Lagrangian submanifolds in Marsden-Weinstein quotients which are fixpoint sets of some antisymplectic involution. For these Lagrangians the Floer homology cannot in general be defined by standard means due to the bubbling phenomenon. To overcome this difficulty we consider moment Floer homology whose boundary operator is defined by counting solutions of the symplectic vortex equations on the strip which have better compactness properties than the original Floer equations.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bc0ccbd54a53bcdbb93c369ffda60fe6b3d8404d

How researchers see this paper

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In Geometry and Topology

1. Frederick J. Bourgeois III
2. M. Abouzaid
3. P. Seidel
4. Kai Cieliebak
5. A. Oancea
6. T. Ekholm
7. Alexander F. Ritter
8. Y. Eliashberg

In Mathematical Physics

1. P. Seidel
2. Frederick J. Bourgeois III
3. M. Abouzaid
4. A. Oancea
5. Kai Cieliebak
6. T. Ekholm
7. Alexander F. Ritter
8. Y. Eliashberg

Citations in the corpus

• Leaf-wise intersections and Rabinowitz Floer homology (2008, background): “ 0 the Rabinowitz action functional AF 0 is Morse-Bott with critical manifold Σ, on which the action functional vanishes. Since the functional only has one critical value the complex of cascades, see [Fra04], computing the Morse-Bott homology HFloc(AF 0 ) equals the Morse complex of the critical man”
• Persistence modules with operators in Morse and Floer theory (2017, methodology): “Finally, one could use Frauenfelder’s approach of cascades [30] to the MorseBott case, which readily yields a persistence module by the same procedure as in [47, 55].”
• Effect of Legendrian surgery (2009, background): “Iˇ/ to describe parts of the differential in a chain complex which computes symplectic homology in Morse–Bott terms following Bourgeois and Oancea [9] (see also Frauenfelder [26] in the case of Morse theory).”
• Persistent homology and Floer-Novikov theory (2015, unknown): “ltered chain isomorphism classification is likely too fine, in that it may depend on auxiliary choices made in the construction of the complex (for instance, in the Morse-Bott complex as constructed in [Fr04], it would depend on the choices of Morse functions on the critical submanifolds of the Morse-”
• Gauged Floer Theory Of Toric Moment Fibers (2010, methodology): “In the case that X has no holomorphic spheres, the gauged Floer theory has better compactness properties than the theory in X//G. Frauenfelder [17] used his gauged Floer theory to prove a version of the ArnoldGivental conjecture in this context.”
• A FLOER HOMOLOGY FOR EXACT CONTACT EMBEDDINGS (2007, methodology): “For a formal definition of gradient flow lines with cascades we refer to [19].”
• An open string analogue of Viterbo functoriality (2007, background): “We adapt their construction to the setting of popsicles, and call the resulting objects cascades (as far as the authors know, this is not related to the use of the same term in [11]).”