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A crossed homomorphism for groups acting on the circle
Shuhei Maruyama
We construct a crossed homomorphism by using a group action on the circle and the Poincaré translation number. We relate it to the Euler class of the action in terms of the Hochsch…
Invariant quasimorphisms for groups acting on the circle and non-equivalence of SCL
Shuhei Maruyama, Takahiro Matsushita, Masato Mimura
We construct invariant quasimorphisms for groups acting on the circle. Furthermore, we provide a criterion for the non-extendablity of the resulting quasimorphisms and an explicit…
Group cocycles on the volume-preserving diffeomorphism group
Shuhei Maruyama
We construct two kinds of group cocycles on the volume-preserving diffeomorphism group. We show that, for the volume-preserving diffeomorphism group of the sphere, one of the cocyc…
The Dixmier-Douady class and an abelian extension of the homeomorphism group
Shuhei Maruyama
Let be a connected topological space and a non-zero cohomology class. A -bundle is a fiber bundle with fiber whose s…
Extensions of quasi-morphisms to the symplectomorphism group of the disk
Shuhei Maruyama
On the group of symplectomorphisms of the disk which are the identity near the boundary, there are homogeneous quasi-morphisms called the Ruelle invarian…
The translation number and quasi-morphisms on groups of symplectomorphisms of the disk
Shuhei Maruyama
On groups of symplectomorphisms of the disk, we construct two homogeneous quasi-morphisms which relate to the Calabi invariant and the flux homomorphism respectively. We also show…
The flux homomorphism and central extensions of diffeomorphism groups
Shuhei Maruyama
Let be a 2-dimensional closed unit disk and the group of symplectomorphisms preserving the origin and the boundary pointwise. We consid…