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.

scholarly journals ON THE GENERALIZED VOLUME CONJECTURE AND REGULATOR

2008 ◽  
Vol 10 (supp01) ◽  
pp. 1023-1032 ◽  
Author(s):  
WEIPING LI ◽  
QINGXUE WANG
Keyword(s):  
Line Bundle ◽  
Chern Class ◽  
Quantization Condition ◽  
Character Variety ◽  
Characteristic Class ◽  
Volume Conjecture ◽  
Smooth Part ◽  
First Chern Class ◽  
Chern Simons ◽  
Secondary Characteristic

In this paper, by using the regulator map of Beilinson-Deligne on a curve, we show that the quantization condition posed by Gukov is true for the SL2(ℂ) character variety of the hyperbolic knot in S3. Furthermore, we prove that the corresponding ℂ*-valued closed 1-form is a secondary characteristic class (Chern-Simons) arising from the vanishing first Chern class of the flat line bundle over the smooth part of the character variety, where the flat line bundle is the pullback of the universal Heisenberg line bundle over ℂ* × ℂ*. Based on this result, we give a reformulation of Gukov's generalized volume conjecture from a motivic perspective.

A High Efficiency Class-E Power Amplifier Over a Wide Power Range Using a Look-Up Table Based Dynamic Biasing Scheme

2015 ◽  
Vol E98.C (4) ◽  
pp. 377-379
Author(s):  
Jonggyun LIM ◽  
Wonshil KANG ◽  
Kang-Yoon LEE ◽  
Hyunchul KU
Keyword(s):  
Power Amplifier ◽  
High Efficiency ◽  
Look Up Table ◽  
Dynamic Biasing ◽  
Class E

A Primer on Mapping Class Groups (PMS-49)

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Graduate Students ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Class Group ◽  
Mapping Class ◽  
Torelli Group ◽  
Surface Bundles ◽  
Surface Homeomorphisms ◽  
Low Dimensional

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. It begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn–Nielsen–Baer–theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

Production of Recombinant Allergens Phl p 1 and Amb a 1 for Detection of Class E Immunoglobulins

2020 ◽  
Vol 46 (6) ◽  
pp. 1221-1228
Author(s):  
O. O. Mikheeva ◽  
M. A. Kostromina ◽  
D. D. Lykoshin ◽  
M. N. Tereshin ◽  
S. K. Zavriev ◽  
...  
Keyword(s):  
Recombinant Allergens ◽  
Amb A 1 ◽  
Class E
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