scholarly journals $L^{2}$ -torsion invariants of a surface bundle over $S^{1}$

2004 ◽  
Vol 56 (2) ◽  
pp. 503-518 ◽  
Author(s):  
Teruaki KITANO ◽  
Takayuki MORIFUJI ◽  
Mitsuhiko TAKASAWA
Keyword(s):  
Surface Bundle

scholarly journals The universal n-pointed surface bundle only has n sections

2019 ◽  
Vol 11 (02) ◽  
pp. 293-309 ◽  
Author(s):  
Lei Chen
Keyword(s):  
Fixed Points ◽  
Surjective Homomorphism ◽  
Independent Interest ◽  
Diffeomorphism Group ◽  
Classifying Space ◽  
Universal Bundle ◽  
Genus Formula ◽  
Surface Bundle ◽  
Hyperelliptic Surface

The classifying space BDiff[Formula: see text] of the orientation-preserving diffeomorphism group of a surface [Formula: see text] of genus [Formula: see text] fixing [Formula: see text] points pointwise has a universal bundle [Formula: see text] The [Formula: see text] fixed points provide [Formula: see text] sections [Formula: see text] of [Formula: see text]. In this paper we prove a conjecture of R. Hain that any section of [Formula: see text] is homotopic to some [Formula: see text]. Let [Formula: see text] be the space of ordered [Formula: see text]-tuple of distinct points on [Formula: see text]. As part of the proof of Hain’s conjecture, we prove a result of independent interest: any surjective homomorphism [Formula: see text] is equal to one of the forgetful homomorphisms [Formula: see text], possibly post-composed with an automorphism of [Formula: see text]. We also classify sections of the universal hyperelliptic surface bundle.

ON FRAMED LINK PRESENTATIONS OF SURFACE BUNDLES

1998 ◽  
Vol 07 (08) ◽  
pp. 1087-1092
Author(s):  
KAZUHIRO ICHIHARA
Keyword(s):  
Orientable Surface ◽  
Closed Orientable Surface ◽  
Surface Bundles ◽  
Fibered Link ◽  
Surface Bundle ◽  
Framed Link

In this paper, we show that every closed orientable surface bundle over the circle is represented by a fibered link in the 3-sphere with framings induced by the fibration of the complement.

scholarly journals BNS INVARIANTS AND ALGEBRAIC FIBRATIONS OF GROUP EXTENSIONS

2021 ◽  
pp. 1-15
Author(s):  
Stefan Friedl ◽  
Stefano Vidussi
Keyword(s):  
Fundamental Group ◽  
Broad Class ◽  
Interesting Case ◽  
Finitely Generated ◽  
Group Extensions ◽  
Finitely Generated Group ◽  
Surface Bundles ◽  
Surface Bundle

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.

scholarly journals Stable rationality of quadric and cubic surface bundle fourfolds

2018 ◽  
Vol 4 (3) ◽  
pp. 732-760 ◽  
Author(s):  
Asher Auel ◽  
Christian Böhning ◽  
Alena Pirutka
Keyword(s):  
Stable Rationality ◽  
Cubic Surface ◽  
Surface Bundle

scholarly journals Virtual surface Bundle groups

2000 ◽  
Vol 62 (3) ◽  
pp. 353-356
Author(s):  
J. A. Hillman
Keyword(s):  
Free Groups ◽  
Type I ◽  
Type Ii ◽  
Surface Bundle ◽  
Torsion Free

We show that all torsion free groups which are virtual surface bundle groups of type I in Johnson's trichotomy may be realised by aspherical closed smooth 4-manifolds. (This was already known for type II.)

scholarly journals Surface bundles over surfaces: new inequalities between signature, simplicial volume and Euler characteristic

2020 ◽  
Author(s):  
Michelle Bucher ◽  
Caterina Campagnolo
Keyword(s):  
Euler Characteristic ◽  
Simplicial Volume ◽  
The Third ◽  
Surface Bundles ◽  
Surface Bundle ◽  
Ramified Coverings ◽  
New Inequalities

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.

A topologically minimal canonical Heegaard splitting of a surface bundle is critical

2018 ◽  
Vol 27 (05) ◽  
pp. 1850034
Author(s):  
Qiang E
Keyword(s):  
Topological Index ◽  
Topological Indices ◽  
Heegaard Splitting ◽  
Genus Formula ◽  
Heegaard Surfaces ◽  
Surface Bundle

Every surface bundle with genus [Formula: see text] fiber has a canonical Heegaard splitting of genus [Formula: see text]. In this paper, we discuss the topological indices of such Heegaard surfaces and prove the canonical Heegaard splitting of a surface bundle is topologically minimal if and only if it is critical, that is, its topological index is 2.

Sign in / Sign up

Export Citation Format

Share Document