2026/01/12 by Takefumi Nosaka
Mathematics · #math.GT #math.AT
We prove that the third integral group homology of both the volume-preserving diffeomorphism group and the strict contactomorphism group of the standard \(3\)-sphere contains \((\mathbb Q/\mathbb Z)2\). The proof constructs two independent locally smooth Chern--Simons-type \(3\)-classes from the volume form and the standard framing of \(S3\). A torsion-controlled local integration method and comparison with the primitive Cheeger--Chern--Simons class also detect \(\mathbb Q/\mathbb Z\) for several spherical space forms and symplectic projective manifolds.