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The group Aut and Out of the fundamental group of a closed Sol 3-manifold
Daciberg Lima Gonçalves, Sérgio Tadao Martins
Let be the fundamental group of a closed Sol 3-manifold. We describe the groups and . We first consider the case where is the fundamental group of a torus…
The cohomology ring of certain families of periodic virtually cyclic groups
Sérgio Tadao Martins, Daciberg Lima Gonçalves, Márcio de Jesus Soares
Let G be a virtually cyclic of the form (Z_a x Z_b) x Z or [Z_a x (Z b x Q_{2^i})] x Z. We compute the integral cohomology ring of G, and then obtain the periodicity of the Farell…
The cohomology ring of the sapphires that admit the Sol geometry
Sérgio Tadao Martins, Daciberg Lima Gonçalves
Let be the fundamental group of a sapphire that admits the Sol geometry and is not a torus bundle. We determine a finite free resolution of over and…
Diagonal approximation and the cohomology ring of the fundamental groups of surfaces
Sergio Tadao Martins, Daciberg Lima Goncalves
We construct finite free resolutions of Z over ZG, where G is the fundamental group of a surface distinct from S^2 and RP^2, and define diagonal approximations for these resolution…
Diagonal approximation and the cohomology ring of torus fiber bundles
Sérgio Tadao Martins
For a torus bundle (S^1 x S^1) -> E -> S^1$, we construct a finite free resolution Z over ZG, where G is the fundamental group of the total space E, and then we compute the cohomol…