2021/07/19 by Kawasaki, Morimichi, Kimura, Mitsuaki, Maruyama, Shuhei +2 · 1 citation
#20F65 #20J05 #20J06 #57M07 #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Topology (math.GT) #Group Theory (math.GR) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2107.08571
For a pair (G,N) of a group G and its normal subgroup N, we consider the space of quasimorphisms and quasi-cocycles on N non-extendable to G. To treat this space, we establish the five-term exact sequence of cohomology relative to the bounded subcomplex. As its application, we study the spaces associated with the kernel of the (volume) flux homomorphism, the IA-automorphism group of a free group, and certain normal subgroups of Gromov-hyperbolic groups. Furthermore, we employ this space to prove that the stable commutator length is equivalent to the stable mixed commutator length for certain pairs of a group and its normal subgroup.