Volumes of Discrete Groups and Topological Complexity of Homology Spheres

Details Volumes of Discrete Groups and Topological Complexity of Homology Spheres Volumes of Discrete Groups and Topological Complexity of Homology Spheres

1995-06-25

arxiv.org/abs/dg-ga/9506010v1

Mathematics

Differential Geometry

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We address two fundamental and well-known problems of Gromov and Lyndon: \demo{Problem A} (Gromov, see [5]). Consider a category $M_n$ of closed manifolds of dimension $n$ with nonzero-degree ways as morphisms. Study a partial order $M \ge N \Leftrightarrow Mor (M, N) \neq \phi$. For which $N$ the degrees of maps $f: M \to N$ are bounded for all $M$? \demo{Problem B} (Lyndon, [12], problem 13). Extend and relate the theories of deficiency, the rate of growth and the Euler-Poincar\'e characteristic. In particular, what influence does the deficiency have on the structure of an infinite group?

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