The lack of counterexamples to Donaldson's 4-6 question
Research gap analysis derived from 3 mathematics papers in our local library.
The gap
The lack of counterexamples to Donaldson's 4-6 question. The limited understanding of the relationship between symplectic structures and deformation equivalence on 4-manifolds.
Evidence profile
Sourced from the stated research gap and future-work section of the source papers, classified as general, spanning 3 journals.
Research trend
Established — well-defined area with open sub-problems.
Supporting evidence — 4 representative gaps
- Symplectic semi-characteristics (2026) · Pacific Journal of Mathematics · doi
The paper identifies a gap in the understanding of the symplectic semi-characteristic of closed 4n-dimensional symplectic manifolds. Prior work did not provide a counting formula for the symplectic semi-characteristic.
generalstated research gapevidence 5/5Keywords: paper identifies gap understanding symplectic semi-characteristic closed n-dimensional - A note on a nontrivial connected component of the space of symplectic structures (2026) · Algebraic & Geometric Topology · doi
The uniqueness question for symplectic structures is still open for closed manifolds in dimension four. There is a lack of examples of nontrivial connected components of the space of symplectic structures standard at infinity in dimension four. Prior work has not addressed the question of uniqueness for open manifolds in dimension four.
generalstated research gapevidence 5/5Keywords: uniqueness question symplectic structures still open closed manifolds - A note on a nontrivial connected component of the space of symplectic structures (2026) · Algebraic & Geometric Topology · doi
Study higher homotopy groups of the space of symplectic structures. Investigate the question of finding nontrivial connected components of the space of symplectic structures for closed manifolds in dimension four. Find a symplectic proof of Question 3.1 directly.
generalfuture-work sectionevidence 5/5Keywords: study higher homotopy groups space symplectic structures investigate - On Donaldson’s 4-6 question (2026) · Geometry & Topology · doi
The lack of counterexamples to Donaldson's 4-6 question. The limited understanding of the relationship between symplectic structures and deformation equivalence on 4-manifolds.
generalstated research gapevidence 5/5Keywords: lack counterexamples donaldson question limited understanding relationship between
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