A complex semigroup that contains the group of diffeomorphisms of the circle

1987 ◽  
Vol 21 (2) ◽  
pp. 160-161 ◽  
Author(s):  
Yu. A. Neretin
Keyword(s):  
Group Of Diffeomorphisms ◽  
Complex Semigroup

scholarly journals Diffeomorphism cocycles over partially hyperbolic systems

2020 ◽  
pp. 1-24
Author(s):  
VICTORIA SADOVSKAYA
Keyword(s):  
Hyperbolic System ◽  
Compact Manifold ◽  
Hyperbolic Systems ◽  
Riemannian Metrics ◽  
Hölder Continuous ◽  
Group Of Diffeomorphisms ◽  
Small Loss ◽  
Partially Hyperbolic ◽  
Loss Of Regularity

Abstract We consider Hölder continuous cocycles over an accessible partially hyperbolic system with values in the group of diffeomorphisms of a compact manifold $\mathcal {M}$ . We obtain several results for this setting. If a cocycle is bounded in $C^{1+\gamma }$ , we show that it has a continuous invariant family of $\gamma $ -Hölder Riemannian metrics on $\mathcal {M}$ . We establish continuity of a measurable conjugacy between two cocycles assuming bunching or existence of holonomies for both and pre-compactness in $C^0$ for one of them. We give conditions for existence of a continuous conjugacy between two cocycles in terms of their cycle weights. We also study the relation between the conjugacy and holonomies of the cocycles. Our results give arbitrarily small loss of regularity of the conjugacy along the fiber compared to that of the holonomies and of the cocycle.

scholarly journals COHOMOLOGY FOR A GROUP OF DIFFEOMORPHISMS OF A MANIFOLD PRESERVING AN EXACT FORM

2006 ◽  
Vol 03 (05n06) ◽  
pp. 1117-1130
Author(s):  
MARK LOSIK ◽  
PETER W. MICHOR
Keyword(s):  
Exact Form ◽  
Group Of Diffeomorphisms

Let M be a G-manifold and ω a G-invariant exact m-form on M. We indicate when these data allow us to construct a cocycle on a group G with values in the trivial G-module ℝ, and when this cocycle is nontrivial.

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