The space of nonextendable quasimorphisms
Abstract
In the present paper, for a pair $(G,N)$ of a group $G$ and its normal subgroup $N$, we consider the space of quasimorphisms and quasicocycles on $N$ nonextendable to $G$. To treat this space, we establish the fiveterm exact sequence of cohomology relative to the bounded subcomplex. As its application, we study the spaces associated with the commutator subgroup of a Gromov hyperbolic group, the kernel of the (volume) flux homomorphism, and the IAautomorphism group of a free group. Furthermore, we employ this space to prove that the stable commutator length is equivalent to the mixed stable commutator length for certain pairs of a group and its normal subgroup.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.08571
 Bibcode:
 2021arXiv210708571K
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Functional Analysis;
 Mathematics  Geometric Topology;
 Mathematics  Symplectic Geometry
 EPrint:
 48 pages, 1 figures. We add Subsection 8.3, where we describe a relation between the 2Kazhdan property and the space of nonextendable quasicocycles