On tori embedded in four-manifolds
type: Item
instance of: scholarly article
title: On tori embedded in four-manifolds
zbMATH Open document ID: 0788.53046
author: Paolo Lisca
published in: Journal of Differential Geometry
publication date: 1998-04-13T00:00:00Z
review text: Let \(M\) be a smooth, closed simply connected 4-manifold with \(b^ +_ 2(M) > 1\) odd. We prove that the existence of a smoothly embedded 2-torus \(T \hookrightarrow M\) with self-intersection \(+1\) implies that the generalized Donaldson polynomials of \(M\) vanish on the orthogonal complement of the homology class represented by \(T\). We show how this implies that there are no such tori inside a smooth simply connected complex surface with geometric genus greater than zero whose minimal model is either elliptic or a complete intersection.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 57R40
Mathematics Subject Classification ID: 81T13
zbMATH DE Number: 444972
zbMATH Keywords: embedded surfaces
zbMATH Keywords: 4-manifold
zbMATH Keywords: Donaldson polynomials
zbMATH Keywords: complex surface
zbMATH Keywords: complete intersection
Wikidata QID: Q115180179
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214454094
OpenAlex ID: W1508072289
DOI: 10.4310/JDG/1214454094
description: scientific article; zbMATH DE number 444972