Universität zu Köln

Ding, Fan, Geiges, Hansjoerg and van Koert, Otto (2012). Diagrams for contact 5-manifolds. J. Lond. Math. Soc.-Second Ser., 86. S. 657 - 683. OXFORD: OXFORD UNIV PRESS. ISSN 0024-6107

Full text not available from this repository.

Abstract

According to Giroux, contact manifolds can be described as open books whose pages are Stein manifolds. For 5-dimensional contact manifolds the pages are Stein surfaces, which permit a description via Kirby diagrams. We introduce handle moves on such diagrams that do not change the corresponding contact manifold. As an application, we derive classification results for subcritically Stein fillable contact 5-manifolds and characterize the standard contact structure on the 5-sphere in terms of such fillings. This characterization is discussed in the context of the Andrews-Curtis conjecture concerning presentations of the trivial group. We further illustrate the use of such diagrams by a covering theorem for simply connected spin 5-manifolds and a new existence proof for contact structures on simply connected 5-manifolds.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Ding, Fan UNSPECIFIED UNSPECIFIED UNSPECIFIED Geiges, Hansjoerg UNSPECIFIED UNSPECIFIED UNSPECIFIED van Koert, Otto UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-478059
DOI:	10.1112/jlms/jds020
Journal or Publication Title:	J. Lond. Math. Soc.-Second Ser.
Volume:	86
Page Range:	S. 657 - 683
Date:	2012
Publisher:	OXFORD UNIV PRESS
Place of Publication:	OXFORD
ISSN:	0024-6107
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language SYMPLECTIC-MANIFOLDS; OPEN BOOKS; HOMOLOGY; KNOTS; TOPOLOGY Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/47805