| __Amazon.com: Books: Metric Structures for Riemannian and Non-Riemannian Spaces : Based on Structures Metriques des ...__ *(Site not responding. Last check: 2007-10-06)* |

| | **Metric** theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to **Riemannian** geometry and algebraic topology, to the theory of infinite groups and probability theory. |

| | This distance organizes **Riemannian** manifolds of all possible topological types into a single connected moduli space, where convergence allows the collapse of dimension with unexpectedly rich geometry, as revealed in the work of Cheeger, Fukaya, Gromov and Perelman. |

| | Also, Gromov found **metric** structure within homotopy theory and thus introduced new invariants controlling combinatorial complexity of maps and spaces, such as the simplicial volume, which is responsible for degrees of maps between manifolds. |

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