Universität zu Köln

Geiges, Hansjoerg and Gonzalo Perez, Jesus (2016). Transversely holomorphic flows and contact circles on spherical 3-manifolds. Enseign. Math., 62 (3-4). S. 527 - 568. ZURICH: EUROPEAN MATHEMATICAL SOC. ISSN 2309-4672

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Abstract

Motivated by the moduli theory of taut contact circles on spherical 3-manifolds, we relate taut contact circles to transversely holomorphic flows. We give an elementary survey of such 1-dimensional foliations from a topological viewpoint. We describe a complex analogue of the classical Godbillon-Vey invariant, the so-called Bott invariant, and a logarithmic monodromy of closed leaves. The Bott invariant allows us to formulate a generalised Gau beta-Bonnet theorem. We compute these invariants for the Poincare foliations on the 3-sphere and derive rigidity statements, including a uniformisation theorem for orbifolds. These results are then applied to the classification of taut contact circles.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Geiges, Hansjoerg UNSPECIFIED UNSPECIFIED UNSPECIFIED Gonzalo Perez, Jesus UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-287817
DOI:	10.4171/LEM/62-3/4-8
Journal or Publication Title:	Enseign. Math.
Volume:	62
Number:	3-4
Page Range:	S. 527 - 568
Date:	2016
Publisher:	EUROPEAN MATHEMATICAL SOC
Place of Publication:	ZURICH
ISSN:	2309-4672
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language 2-DIMENSIONAL ORBIFOLDS; SPHERES Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/28781