The space of non-extendable quasimorphisms
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2021
- DOI:
- 10.48550/arXiv.2107.08571
- arXiv:
- arXiv:2107.08571
- Bibcode:
- 2021arXiv210708571K
- Keywords:
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- Mathematics - Group Theory;
- Mathematics - Functional Analysis;
- Mathematics - Geometric Topology;
- Mathematics - Symplectic Geometry;
- 20J06;
- 20J05;
- 20F65;
- 57M07
- E-Print:
- 60 pages, 1 figure. Minor revision, errors corrected and explanations brushed up