On a proof of the JSJ theorem.
Let be a compact, orientable, irreducible 3-manifold with a torus. We show that there can be infinitely many slopes on realized by the boundary curves of immersed, incompressible, - incompressible surfaces in which are embedded in a neighborhood of .
We prove that the semistability growth of hyperbolic groups is linear, which implies that hyperbolic groups which are sci (simply connected at infinity) have linear sci growth. Based on the linearity of the end-depth of finitely presented groups we show that the linear sci is preserved under amalgamated products over finitely generated one-ended groups. Eventually one proves that most non-uniform lattices have linear sci.
We address the following question: How different can closed, oriented 3-manifolds be if they become homeomorphic after taking a product with a sphere? For geometric 3-manifolds this paper provides a complete answer to this question. For possibly non-geometric 3-manifolds, we establish results which concern 3-manifolds with finite fundamental group (i.e., 3-dimensional fake spherical space forms) and compare these results with results involving fake spherical space forms of higher...