The exact sequence in the homology of groups with integral coefficients modulo associated to two normal subgroups
Let be a polynomial ring in variables and let be a strictly increasing sequence of integers. Boij and Söderberg conjectured the existence of graded -modules of finite length having pure free resolution of type in the sense that for the -th syzygy module of has generators only in degree .This paper provides a construction, in characteristic zero, of modules with this property that are also -equivariant. Moreover, the construction works over rings of the form where is a polynomial...
We prove that the Fibonacci morphism is an automorphism of infinite order of free Burnside groups for all odd and even .
We prove that the Fibonacci morphism is an automorphism of infinite order of free Burnside groups for all odd and even .
Given a maximal arithmetic Kleinian group , we compute its finite subgroups in terms of the arithmetic data associated to by Borel. This has applications to the study of arithmetic hyperbolic 3-manifolds.