77 research outputs found
Simplicial volume with -coefficients
For primes , we investigate an -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
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