Simplicial volume with Fp\mathbb{F}_p-coefficients

For primes $p$, we investigate an $\mathbb{F}_p$-version of simplicial volume and compare these invariants with their siblings over other coefficient rings. We will also consider the associated gradient invariants, obtained by stabilisation along finite coverings. Throughout, we will discuss the relation between such simplicial volumes and Betti numbers.Comment: 21 pages; v2: small changes; to appear in Period. Math. Hun

Measure homology and singular homology are isometrically isomorphic

Measure homology is a variation of singular homology designed by Thurston in his discussion of simplicial volume. Zastrow and Hansen showed independently that singular homology (with real coefficients) and measure homology coincide algebraically on the category of CW-complexes. It is the aim of this paper to prove that this isomorphism is isometric with respect to the l^1-seminorm on singular homology and the seminorm on measure homology induced by the total variation. This, in particular, implies that one can calculate the simplicial volume via measure homology -- as already claimed by Thurston. For example, measure homology can be used to prove the proportionality principle of simplicial volume.Comment: 20 pages, typos corrected, see also http://www.math.uni-muenster.de/u/clara.loeh/preprints.html, accepted by Mathematische Zeitschrift -- the original publication is available at www.springerlink.com (http://dx.doi.org/10.1007/s00209-005-0905-7

Finite functorial semi-norms and representability

Functorial semi-norms are semi-normed refinements of functors such as singular (co)homology. We investigate how different types of representability affect the (non-)triviality of finite functorial semi-norms on certain functors or classes. In particular, we consider representable functors, generalised cohomology theories, and so-called weakly flexible homology classes in singular homology and l1-homology.Comment: 18 pages; v3: small changes as suggested by the referee; v2: clarified Example 4.3, added referenc