2024/12/24 by KyeongRo Kim, Kim, KyeongRo, Shuhei Maruyama +1 · 1 citation
Mathematics · #Mathematical Dynamics and Fractals #Advanced Topics in Algebra #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2412.18466
The existence of quasimorphisms on groups of homeomorphisms of manifolds has been extensively studied under various regularity conditions, such as smooth, volume-preserving, and symplectic. However, in this context, nothing is known about groups of `area'-preserving diffeomorphisms on non-orientable manifolds. In this paper, we initiate the study of groups of density-preserving diffeomorphisms on non-orientable manifolds. Here, the density is a natural concept that generalizes volume without concerning orientability. We show that the group of density-preserving diffeomorphisms on the Möbius band admits countably many unbounded quasimorphisms which are linearly independent. Along the proof, we show that groups of density preserving diffeomorphisms on compact, connected, non-orientable surfaces with non-empty boundary are weakly contractible.