Dexie Lin

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math.DG2023

A Kodaira type conjecture on almost complex 4 manifolds

Dexie Lin

Not long ago, Cirici and Wilson defined a Dolbeault cohomology on almost complex manifolds to answer Hirzebruch's problem. In this paper, we define a refined Dolbeault cohomology o…

math.DG2019

Seiberg-Witten equation on a manifold with rank $2$ -foliation

Dexie Lin

Let $M$ be a closed oriented $4$ -manifold admitting a rank- $2$ oriented foliation with a metric of leafwise positive scalar curvature. If $b^{+} > 1$ , then we will show that the Seiber…

math.DG2019

Index of transverse Dirac operator and cohomotopy Seiberg-Witten invariant for codimension $4$ Riemannian foliation

Dexie Lin

For closed manifolds endowed with a Riemannian foliation of codimension $4$ , one can define a transversal Seiberg-Witten map. We show that there is a finite dimensional approximati…

A Kodaira type conjecture on almost complex 4 manifolds

Seiberg-Witten equation on a manifold with rank 2-foliation

Index of transverse Dirac operator and cohomotopy Seiberg-Witten invariant for codimension 4 Riemannian foliation

Seiberg-Witten equation on a manifold with rank $2$ -foliation

Index of transverse Dirac operator and cohomotopy Seiberg-Witten invariant for codimension $4$ Riemannian foliation