An obstruction to sliceness via contact geometry and ``classical'' gauge theory
type: Item
instance of: scholarly article
title: An obstruction to sliceness via contact geometry and ``classical'' gauge theory
zbMATH Open document ID: 0843.57011
DOI: 10.1007/BF01245177
author: L. Rudolph
published in: Inventiones Mathematicae
publication date: 1996-08-18T00:00:00Z
full work available at URL: https://eudml.org/doc/144251
review text: The author shows that if a knot has a non-negative maximal Thurston-Bennequin invariant, then it is not slice. The method is a combination of 3-dimensional contact geometry and 4-dimensional ``classical'' gauge theory à la Donaldson. This is supposed to be in contrast to the new gauge theoretic techniques of Kronheimer and Mrowka which lead to the proof of the Thom conjecture and the Bennequin inequality for the slice genus of a knot. This inequality implies the first mentioned result. As a nice corollary of his result the author mentions that the simplest Casson-handle (with one kink in every step) is non-standard if all kinks have the same sign. This result was first obtained by Ž. Bižaca and is conjectured for arbitrary signs of the kinks.
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57N13
zbMATH DE Number: 763284
zbMATH Keywords: knots
zbMATH Keywords: slice knots
zbMATH Keywords: gauge theory
zbMATH Keywords: contact structures
Wikidata QID: Q60148876
reviewed by: Peter Teichner
MaRDI profile type: Publication
cites work: Q3692516
cites work: Complex curves and surgery
cites work: Q4288662
cites work: Classification of overtwisted contact structures on 3-manifolds
cites work: Gauge theory for embedded surfaces. I
cites work: Braided surfaces and Seifert ribbons for closed braids
cites work: Q3740652
cites work: A congruence between link polynomials
cites work: Constructions of quasipositive knots and links. III: A characterization of quasipositive Seifert surfaces
cites work: QUASIPOSITIVE ANNULI (CONSTRUCTIONS OF QUASIPOSITIVE KNOTS AND LINKS, IV)
cites work: Q4028067
cites work: Quasipositivity as an obstruction to sliceness
description: scientific article; zbMATH DE number 763284