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November 2019 Topology of Kähler Manifolds with Weakly Pseudoconvex Boundary
Brian Weber
Michigan Math. J. 68(4): 727-742 (November 2019). DOI: 10.1307/mmj/1563847454

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.

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Brian Weber. "Topology of Kähler Manifolds with Weakly Pseudoconvex Boundary." Michigan Math. J. 68 (4) 727 - 742, November 2019. https://doi.org/10.1307/mmj/1563847454

Information

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

zbMATH: 07155046
MathSciNet: MR4029626
Digital Object Identifier: 10.1307/mmj/1563847454

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Rights: Copyright © 2019 The University of Michigan

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Vol.68 • No. 4 • November 2019
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