Zhang, Weiyi (2017) Geometric structures, Gromov Norm and Kodaira dimensions. Advances in Mathematics, 308 . pp. 1-35. doi:10.1016/j.aim.2016.12.005 ISSN 0001-8708.

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Abstract

We define the Kodaira dimension for 3-dimensional manifolds
through Thurston’s eight geometries, along with a classification in
terms of this Kodaira dimension. We show this is compatible with other
existing Kodaira dimensions and the partial order defined by non-zero
degree maps. For higher dimensions, we explore the relations of geometric structures and mapping orders with various Kodaira dimensions and other invariants. Especially, we show that a closed geometric 4-manifold has nonvanishing Gromov norm if and only if it has geometry H 2 × H 2 , H 2 (C) or H 4.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Complex manifolds, Symplectic manifolds
Journal or Publication Title:	Advances in Mathematics
Publisher:	Academic Press
ISSN:	0001-8708
Official Date:	21 February 2017
Dates:	Date Event 21 February 2017 Published 12 December 2016 Accepted 16 December 2016 Available
Volume:	308
Page Range:	pp. 1-35
DOI:	10.1016/j.aim.2016.12.005
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	15 December 2016
Date of first compliant Open Access:	16 December 2017
Funder:	American Mathematical Society, Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	EP/N002601/1
Open Access Version:	ArXiv

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