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arXiv · 2412.18466

Quasimorphisms on the group of density preserving diffeomorphisms of the Möbius band

KyeongRo Kim·Shuhei Maruyama
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Abstract

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.

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KyeongRo Kim, Shuhei Maruyama. 2025-04-14. Quasimorphisms on the group of density preserving diffeomorphisms of the Möbius band. https://arxiv.org/abs/2412.18466

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