Universität zu Köln

Marinkovic, A. and Pabiniak, M. (2016). On displaceability of pre-Lagrangian toric fibers in contact toric manifolds. Int. J. Math., 27 (14). SINGAPORE: WORLD SCIENTIFIC PUBL CO PTE LTD. ISSN 1793-6519

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Abstract

In this paper, we analyze displaceability of pre-Lagrangian toric fibers in contact toric manifolds. While every symplectic toric manifold contains at least one non-displaceable Lagrangian toric fiber and infinitely many displaceable ones, we show that this is not the case for contact toric manifolds. More precisely, we prove that for the contact toric manifolds S2d-1(d >= 2) and T-k x S2d+k-1(d >= 1) all pre-Lagrangian toric fibers are displaceable, and that for all contact toric manifolds for which the toric action is free, except possibly non-trivial T-3-bundles over S-2, all pre-Lagrangian toric fibers are non-displaceable. Moreover, we also prove that if for a compact connected contact toric manifold all but finitely many pre-Lagrangian toric fibers are non-displaceable then the action is necessarily free. On the other hand, as we will discuss, displaceability of all pre-Lagrangian toric fibers seems to be related to the non-orderability of the underlying contact manifolds.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Marinkovic, A. UNSPECIFIED UNSPECIFIED UNSPECIFIED Pabiniak, M. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-253472
DOI:	10.1142/S0129167X16501135
Journal or Publication Title:	Int. J. Math.
Volume:	27
Number:	14
Date:	2016
Publisher:	WORLD SCIENTIFIC PUBL CO PTE LTD
Place of Publication:	SINGAPORE
ISSN:	1793-6519
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language CONTACTOMORPHISM GROUPS; MAXIMAL TORI; INTERSECTIONS; HOMOLOGY Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/25347