ON THE DUALITY BETWEEN l-HOMOLOGY AND BOUNDED COHOMOLOGY
نویسنده
چکیده
We modify the definition of l-homology and argue why our definition is more adequate than the classical one. While we cannot reconstruct the classical l-homology from the new definition for various reasons, we can reconstruct its Hausdorffification so that no information concerning semi-norms is lost. We obtain an axiomatic characterization of our l-homology as a universal δ-functor and prove that it is pre-dual to our definition of bounded cohomology. We thus answer a question raised by Löh in her thesis. Moreover, we prove Gromov’s theorem and the Matsumoto-Morita conjecture in our context.
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