The minimal genus problem
type: Item
instance of: scholarly article
title: The minimal genus problem
zbMATH Open document ID: 0894.57013
published in: Expositiones Mathematicae
publication date: 1998-03-24T00:00:00Z
review text: This expository article gives a survey of recent progress on the the so-called minimal genus problem. The problem is the following: given a second cohomology class of a smooth four-manifold, what is the minimal genus of an embedded surface which represents the given class? The recent progress on this question has been driven mainly by the emergence of Seiberg-Witten theory. Indeed one of the very first applications of the Seiberg-Witten equations was in Kronheimer and Mrowka's proof the Thom conjecture (which gives explicit lower bound for the genus of an embedded surface representing a given cohomology class). Lawson's review focuses largely on the developments resulting from Seiberg-Witten theory, and includes background material on this important new subject.
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 57R57
Mathematics Subject Classification ID: 57R40
Mathematics Subject Classification ID: 57R95
zbMATH DE Number: 1121250
zbMATH Keywords: minimal genus
zbMATH Keywords: Seiberg-Witten equations
zbMATH Keywords: Thom conjecture
author: Terry Lawson
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1121250