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Updated: Aug 6, 2026
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Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
Relative Thom conjectures, symplectic and beyond
Matthew Hedden1, Katherine Raoux2
1Department of Mathematics, Michigan State University, East Lansing, MI 48824.
Summary
We found a criterion for almost complex curves to minimize genus in 4-manifolds. This work provides obstructions to links bounding symplectic surfaces and has implications for contact manifold geometry.
Area of Science:
- Symplectic Geometry
- Topology
- 4-Manifold Theory
Background:
- Almost complex curves and their homology classes in 4-manifolds.
- The significance of genus minimization for surfaces.
- The relationship between symplectic structures and topology.
Purpose of the Study:
- To establish a criterion for genus minimization of almost complex curves.
- To affirm the relative symplectic Thom conjecture.
- To explore obstructions to links bounding symplectic surfaces.
Main Methods:
- Developing a criterion for genus minimization.
- Utilizing knot Floer homology for obstructions.
- Applying results to knots in contact manifolds.
Main Results:
- A criterion ensuring bounded almost complex curves minimize genus.
- Affirmation of the relative symplectic Thom conjecture.
- Obstructions from knot Floer homology to links bounding symplectic surfaces.
Conclusions:
- Symplectic surfaces in thickened contact 3-manifolds with nonzero Ozsváth-Szabó invariant minimize slice genus.
- Conjecture that this occurs precisely when the contact structure is tight.
- Tightness may be a symplecto-geometric notion.
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