The Michigan Mathematical Journal

Topology of Kähler Manifolds with Weakly Pseudoconvex Boundary

Brian Weber

Advance publication

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1563847454

Digital Object Identifier
doi:10.1307/mmj/1563847454

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

Citation

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


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