CHARACTERISTIC CLASSES OF SURFACE BUNDLES AND BOUNDED COHOMOLOGY

1988 ◽  
pp. 233-257 ◽  
Author(s):  
S. Morita
Keyword(s):  
Characteristic Classes ◽  
Bounded Cohomology ◽  
Surface Bundles

scholarly journals Characteristic classes of surface bundles

1987 ◽  
Vol 90 (3) ◽  
pp. 551-577 ◽  
Author(s):  
Shigeyuki Morita
Keyword(s):  
Characteristic Classes ◽  
Surface Bundles

ON THE FIRST MORITA-MUMFORD CLASS OF SURFACE BUNDLES OVER S1 AND THE ROCHLIN INVARIANT

2000 ◽  
Vol 09 (02) ◽  
pp. 179-186 ◽  
Author(s):  
TERUAKI KITANO
Keyword(s):  
Characteristic Class ◽  
Bounded Cohomology ◽  
Spin Structures ◽  
Surface Bundles ◽  
Secondary Characteristic ◽  
Class E

We consider the first Morita-Mumford class e1 of surface bundles over S1 as a bounded cohomology over Z. It is trivial in general. However in some class of surface bundles over S1 with spin structures, [Formula: see text] makes sense as a characteristic class of them and it is just the Rochlin invariant of such a 3-manifold. It gives a description of the Rochlin invariant as a secondary characteristic class.

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