The Michigan Mathematical Journal

Topology of Kähler Manifolds with Weakly Pseudoconvex Boundary

Brian Weber

Advance publication

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We study Kähler manifolds-with-boundary, not necessarily compact, with weakly pseudoconvex boundary, each component of which is compact. If such a manifold K has l2 boundary components (possibly l=), then it has the first Betti number at least l1, and the Levi form of any boundary component is zero. If K has l1 pseudoconvex boundary components and at least one nonparabolic end, then the first Betti number of K is at least l. In either case, any boundary component has a nonvanishing first Betti number. If K has one pseudoconvex boundary component with vanishing first Betti number, then the first Betti number of K is also zero. Especially significant are applications to Kähler ALE manifolds and to Kähler 4-manifolds. This significantly extends prior results in this direction (e.g., those of Kohn and Rossi) and uses substantially simpler methods.

Article information

Michigan Math. J., Advance publication (2019), 16 pages.

Received: 14 August 2017
Revised: 4 April 2019
First available in Project Euclid: 23 July 2019

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Digital Object Identifier

Primary: 53C55, 53C23, 31C12, 31C10, 58J99


Weber, Brian. Topology of Kähler Manifolds with Weakly Pseudoconvex Boundary. Michigan Math. J., advance publication, 23 July 2019. doi:10.1307/mmj/1563847454.

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