Non-orientable surfaces have stably unbounded homeomorphism group
Building on recent work of Bowden, Hensel and Webb, we prove that the groups of homeomorphisms of the real projective plane and Möbius strip which are isotopic to the identity have an infinite dimensional space of non-trivial homogeneous quasi-morphisms. In particular, we show that they are stably unbounded, completing the answer to a question posed by Burago, Ivanov and Polterovich on the boundedness of diffeomorphism groups of surfaces.
math.GR↗