Characteristic classes of surface bundles

Morita, Shigeyuki

doi:10.1007/bf01389178

Cited by 175 publications

(152 citation statements)

References 22 publications

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“…We begin by recalling some generalities about surface bundles and their sections, which for the most part can be found in [17]. Let Γ h = Diff + (Σ h )/Diff 0 (Σ h ) denote the mapping class group of an oriented Riemann surface Σ h of genus h. By the classical result of Earle and Eells the identity component Diff 0 (Σ h ) is contractible in the C ∞ -topology if h ≥ 2 (cf.…”

Section: Surface Bundles and Boundedness Of The Vertical Euler Classmentioning

confidence: 99%

On Closed Leaves of Foliations, Multisections and Stable Commutator Lengths

Bowden

2011

J. Topol. Anal.

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We give examples of foliations that answer two questions posed by Mitsumatsu and Vogt about the genus minimizing properties of closed leaves of 2-dimensional foliations on 4-manifolds. By studying stable commutator lengths in certain stable mapping class groups, we also answer an asymptotic version of another question of theirs concerning bounds on self-intersection numbers of multisections in surface bundles.

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Section: Surface Bundles and Boundedness Of The Vertical Euler Classmentioning

confidence: 99%

On Closed Leaves of Foliations, Multisections and Stable Commutator Lengths

Bowden

2011

J. Topol. Anal.

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“…The case n D 2 of Theorem A and Theorem B is a well-known result that was first established by Miller [26] and Morita [28] and we make essential use of this in our proof.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 80%

“…B and so the images of Ä E can be viewed as characteristic classes of manifold bundles, which we call generalized Miller-MoritaMumford classes or MMM-classes. Miller [26], Morita [28] and Mumford [30] first studied these classes in the 2-dimensional case.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

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Algebraic independence of generalized MMM–classes

Ebert

2011

Algebr. Geom. Topol.

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The generalized Miller-Morita-Mumford classes (MMM classes) of a smooth oriented manifold bundle are defined as the image of the characteristic classes of the vertical tangent bundle under the Gysin homomorphism. We show that if the dimension of the manifold is even, then all MMM-classes in rational cohomology are nonzero for some bundle. In odd dimensions, this is also true with one exception: the MMM-class associated with the Hirzebruch L-class is always zero. Moreover, we show that polynomials in the MMM-classes are also nonzero. We also show a similar result for holomorphic fibre bundles and for unoriented bundles. 55R40

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“…As shown by Morita [15,Lemma 4.1], after passing to a pull-back cover (which in our case will again be over T 2 ), one can fiberwise cover the latter by a surface bundleF →Xf →B, where the restriction to fibers are the prescribed covering p :F → F . There is a finite covering p :F → F which lifts α to n disjoint loops α 1 , .…”

Section: Fibering Over a Surfacementioning

confidence: 95%