An Isometry Between Measure Homology and Singular Homology

Details An Isometry Between Measure Homology and Singular Homology An Isometry Between Measure Homology and Singular Homology

2004-01-17

arxiv.org/abs/math/0401211v3

Mathematics

Geometric Topology

This paper has been withdrawn due to an error. A correct proof was obtained by Clara Loeh in her thesis. See: math.AT/0504103.

Scientific paper

In Thurston's notes, he gives two different definitions of the Gromov norm (also called simplicial volume) of a manifold and states that they are equal but does not prove it. Gromov proves it in the special case of hyperbolic manifolds as a consequence of his proof that simplicial volume is proportional to volume. We give a proof for all differentiable manifolds. This version corrects a few typos in an earlier version and formally proves the theorem for differentiable manifolds rather than locally finite simplicial complexes (but very few actual changes have been made).

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