Finite functorial semi-norms and representability

Abstract

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.

18 pages; v3: small changes as suggested by the referee; v2: clarified Example 4.3, added reference

References in corpus (5)

• Fundamental classes not representable by products
• Universal Realisators for Homology Classes
• Mapping degrees of self-maps of simply-connected manifolds
• Integral foliated simplicial volume of hyperbolic 3-manifolds
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Cited by in corpus (2)

• Ideal simplicial volume of manifolds with boundary
• Exotic finite functorial semi-norms on singular homology