5 papers
Higher-dimensional generalization of Youngs' theorem and circular colorings
Kengo Enami, Takahiro Matsushita
In 1996, Youngs proved that any quadrangulation of the real projective plane is not 3-chromatic. This result has been extended in various directions over the years, including to ot…
Flux homomorphism and bilinear form constructed from Shelukhin's quasimorphism
Morimichi Kawasaki, Mitsuaki Kimura, Shuhei Maruyama +2
Given a closed connected symplectic manifold , we construct an alternating -bilinear form on the real first cohomol…
Non-extendablity of Shelukhin's quasimorphism and non-triviality of Reznikov's class
Morimichi Kawasaki, Mitsuaki Kimura, Shuhei Maruyama +2
Shelukhin constructed a quasimorphism on the universal covering of the group of Hamiltonian diffeomorphisms for a general closed symplectic manifold. In the present paper, we prove…
Relative simplicity of the universal coverings of transformation groups and Tsuboi's metric
Morimichi Kawasaki, Mitsuaki Kimura, Hiroki Kodama +3
Many transformation groups on manifolds are simple, but their universal coverings are not. In the present paper, we study the concept of relatively simple group, that is, a group w…
Invariant quasimorphisms and generalized mixed Bavard duality
Morimichi Kawasaki, Mitsuaki Kimura, Shuhei Maruyama +2
This article provides an expository account of the celebrated duality theorem of Bavard and three its strengthenings. The Bavard duality theorem connects scl (stable commutator len…