2024/04/23 by Masamitsu Aoki, Aoki, Masamitsu
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2404.14752
openalex publication_date 2024/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the second bounded cohomology of the free product of racks and quandles is infinite-dimensional as a real vector space. This is similar to the case of groups. As a corollary, we show that the second bounded cohomology of the free rack and the free quandle is infinite-dimensional. We also give another proof of this corollary using homogeneous group quasimorphisms.