surface bundles
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Author(s):  
Stefan Friedl ◽  
Stefano Vidussi

Abstract Let G be a finitely generated group that can be written as an extension $$ \begin{align*} 1 \longrightarrow K \stackrel{i}{\longrightarrow} G \stackrel{f}{\longrightarrow} \Gamma \longrightarrow 1 \end{align*} $$ where K is a finitely generated group. By a study of the Bieri–Neumann–Strebel (BNS) invariants we prove that if $b_1(G)> b_1(\Gamma ) > 0$ , then G algebraically fibres; that is, admits an epimorphism to $\Bbb {Z}$ with finitely generated kernel. An interesting case of this occurrence is when G is the fundamental group of a surface bundle over a surface $F \hookrightarrow X \rightarrow B$ with Albanese dimension $a(X) = 2$ . As an application, we show that if X has virtual Albanese dimension $va(X) = 2$ and base and fibre have genus greater that $1$ , G is noncoherent. This answers for a broad class of bundles a question of J. Hillman ([9, Question 11(4)]). Finally, we show that there exist surface bundles over a surface whose BNS invariants have a structure that differs from that of Kodaira fibrations, determined by T. Delzant.





2021 ◽  
pp. 1-25
Author(s):  
Matthias Paulsen


2021 ◽  
Vol 17 (2) ◽  
pp. 649-669
Author(s):  
Andrew Kresch ◽  
Yuri Tschinkel


2020 ◽  
pp. 179-209
Author(s):  
Darryl McCullough
Keyword(s):  


Author(s):  
Michelle Bucher ◽  
Caterina Campagnolo

AbstractWe present three new inequalities tying the signature, the simplicial volume and the Euler characteristic of surface bundles over surfaces. Two of them are true for any surface bundle, while the third holds on a specific family of surface bundles, namely the ones that arise through ramified coverings. These are among the main known examples of bundles with non-zero signature.



2020 ◽  
Vol 116 (2) ◽  
pp. 349-391
Author(s):  
Sam Nariman


2020 ◽  
Vol 102 (3) ◽  
pp. 1178-1222
Author(s):  
Mahan Mj
Keyword(s):  


2020 ◽  
Vol 67 (02) ◽  
pp. 1
Author(s):  
Nick Salter ◽  
Bena Tshishiku


2020 ◽  
Vol 296 (3-4) ◽  
pp. 1081-1100
Author(s):  
Andrew Kresch ◽  
Yuri Tschinkel
Keyword(s):  


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