Local-to-Global Inequality for Spectral Invariants
Author Information
Author(s): Lev Buhovsky, Shira Tanny
Primary Institution: Weizmann Institute of Science
Hypothesis
Does there exist a closed symplectic manifold and disjointly supported Hamiltonians such that the max-inequality does not hold?
Conclusion
The max-inequality holds for all quantum homology classes under certain conditions on the connected components of the support.
Supporting Evidence
- The study presents the first examples of a max-inequality for Hamiltonians not supported in domains with contact-type boundaries.
- The results extend previous works on locality phenomena of spectral invariants.
- The methods used are expected to be applicable to any closed symplectic manifold.
Takeaway
This study shows that when certain conditions are met, we can extend a local property of Hamiltonians to a global one, which is important in understanding their behavior in symplectic geometry.
Methodology
The study uses Floer homology and spectral invariants to analyze Hamiltonians on semipositive symplectic manifolds.
Limitations
The results are primarily applicable to semipositive symplectic manifolds and may not extend to all types of manifolds.
Digital Object Identifier (DOI)
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