2017/10/09 by Heuer, Nicolaus
#FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1710.03193
The theory of bounded cohomology of groups has many applications. A key open problem is to compute the full bounded cohomology Hbn(F, R) of a non-abelian free group F with trivial real coefficients. It is known that Hbn(F,R) is trivial for n=1 and uncountable dimensional for n=2,3, but remains unknown for any n ≥ 4. For n=4, one may construct classes by taking the cup product α∪ β∈ Hb4(F, R) between two 2-classes α, β∈ H2b(F, R). However, we show that all such cup products are trivial if α and β are classes induced by the quasimorphisms defined by Brooks or Rolli.