Donaldson invariants of 4-manifolds with simple type
type: Item
instance of: scholarly article
title: Donaldson invariants of 4-manifolds with simple type
zbMATH Open document ID: 0863.57021
author: Ronald Fintushel
author: Ronald Stern
published in: Journal of Differential Geometry
publication date: 1997-05-27T00:00:00Z
review text: Let \(X\) be a simply-connected 4-manifold of simple type. The authors give a proof of Kronheimer-Mrowka's structure theorem for the Donaldson series of \(X\) which avoids the use of singular connections. Furthermore they prove a result analogous to Kronheimer-Mrowka's lower bound for the genus of embedded surfaces of non-negative self-intersection: the smooth surface is replaced by an immersed sphere, possibly of negative self-intersection. In fact two results are the key ingredients in the proof of the structure theorem: the blow-up formula for simple type 4-manifolds (previously proved by Kronheimer-Mrowka and the authors), and results on the effect on the Donaldson series of embedded spheres of negative self-intersection which are proved in this paper.
Mathematics Subject Classification ID: 57R19
Mathematics Subject Classification ID: 57N13
zbMATH DE Number: 892615
zbMATH Keywords: 4-manifold
zbMATH Keywords: Donaldson series
zbMATH Keywords: genus
zbMATH Keywords: embedded surfaces
reviewed by: Kieran G. O'Grady
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214457550
OpenAlex ID: W1577309380
Wikidata QID: Q115177850
DOI: 10.4310/JDG/1214457550
description: scientific article; zbMATH DE number 892615