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About higher graph manifolds

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In geometric group theory, one of the central questions is to understand what algebraic properties are invariant under quasi-isometries. In this direction, in recent years there has been a lot of work on proving results in rigidity for non-positively curved spaces. In this talk we will study a family of higher graph manifolds and some of its properties that are invariant under quasi-isometries. We will show that isomorphisms between fundamental groups of higher graph manifolds preserve the decomposition into pieces. In addition, for the subfamily of those manifolds called cusp-decomponsable manifolds, we will also show that the inclusion of walls and pieces induces quasi-isometric embeddings.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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