2025/03/28 by Thorben Kastenholz, Kastenholz, Thorben
Mathematics · #20J06 #57K40 #57M60 #57N40 #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #Bounded function #Codimension #Cohomology #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Group cohomology #Homotopy and Cohomology in Algebraic Topology #Linear subspace #Order (exchange) #Submanifold
paper · pdf · doi:10.48550/arxiv.2503.22511
openalex publication_date 2025/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this note we prove that the fouth bounded cohomology of non-abelian free groups with trivial real coefficients is non-zero. In order to prove this, we establish a splitting argument whose simplest form is as follows: Let M denote an n-manifold of non-zero simplicial volume and S a codimension two submanifold of M, then one can conclude that the n-th bounded cohomology of the fundamental group of M ∖ S is non-zero. While in this note this approach is only used for degree 4. There is no reason to expect that this approach and its generalizations is not suitable to prove the non-vanishing of higher degrees or the bounded cohomology of different groups as well.