On the topology of Symplectic Calabi-Yau 4-manifoldsReportar como inadecuado



 On the topology of Symplectic Calabi-Yau 4-manifolds


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Let M be a 4-manifold with residually finite fundamental group G having b 1G 0. Assume that M carries a symplectic structure with trivial canonical class K = 0 in H^2M. 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 $ is determined up to homotopy and, in favorable circumstances, up to homeomorphism by its fundamental group. This is analogous to what was proven 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.



Autor: Stefan Friedl; Stefano Vidussi

Fuente: https://archive.org/







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