Journal of Topology· 2026Q1
Exact orbifold fillings of contact manifolds
- 1citations
- Q1SCImago
- 2026year
Short summary
Researchers define symplectic cohomology for exact orbifold fillings using classical techniques and Floer theories, yielding non-existence and uniqueness results for singularities.
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Key points
- Symplectic cohomology is defined for exact orbifold fillings using classical techniques and Floer theories.
- Moduli spaces of pseudo-holomorphic/Floer curves in orbifolds are studied to derive results on singularities.
- Non-existence, restriction, and uniqueness results are obtained for orbifold singularities in exact orbifold fillings.
- Pairs of contact manifolds without exact cobordisms are shown to exist in dimensions >= 3, and without exact orbifold cobordisms in dimensions >= 5.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We study exact orbifold fillings of contact manifolds using Floer theories. Motivated by Chen–Ruan's orbifold Gromov–Witten invariants, we define symplectic cohomology of an exact orbifold filling as a group using classical techniques, that is, choosing generic almost complex structures. By studying moduli spaces of pseudo‐holomorphic/Floer curves in orbifolds, we obtain various non‐existence, restrictions and uniqueness results for orbifold singularities of exact orbifold fillings of many contact manifolds. For example, we show that exact orbifold fillings of always have exactly one singularity modeled on if . Lastly, we show that in dimension at least 3 there are pairs of contact manifolds without exact cobordisms in either direction, and that the same holds for exact orbifold cobordisms in dimension at least 5.
The authors' abstract, as published at the source. Journal of Topology, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics