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Friedl, Stefan and Vidussi, Stefano (2013). On the topology of symplectic Calabi-Yau 4-manifolds. J. Topol., 6 (4). S. 945 - 955. HOBOKEN: WILEY. ISSN 1753-8424

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Abstract

Let M be a 4-manifold with residually finite fundamental group G having b(1)(G) > 0. Assume that M carries a symplectic structure with trivial canonical class K=0 is an element of H-2(M). Using a theorem of Bauer and Li, together with some classical results in 4-manifold topology, we show that for a large class of groups M is determined up to homotopy and, in favorable circumstances, up to homeomorphism by its fundamental group. This is analogous to what was proved by Morgan-Szabo in the case of b(1)=0 and provides further evidence to the conjectural classification of symplectic 4-manifolds with K=0. As a side, we obtain a result that has some independent interest, namely the fact that the fundamental group of a surface bundle over a surface is large, except for the obvious cases.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Friedl, Stefan UNSPECIFIED UNSPECIFIED UNSPECIFIED Vidussi, Stefano UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-471558
DOI:	10.1112/jtopol/jtt020
Journal or Publication Title:	J. Topol.
Volume:	6
Number:	4
Page Range:	S. 945 - 955
Date:	2013
Publisher:	WILEY
Place of Publication:	HOBOKEN
ISSN:	1753-8424
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language FINITE COVERS; 3-MANIFOLDS; SURFACES; COMPLEX Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/47155