Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-14T02:43:46.125Z Has data issue: false hasContentIssue false
  • English
  • Français

EXOTIC FINITE FUNCTORIAL SEMI-NORMS ON SINGULAR HOMOLOGY

Part of: Topological manifolds Homology and cohomology theories

Published online by Cambridge University Press:  20 June 2018

DANIEL FAUSER  and
CLARA LÖH
DANIEL FAUSER
Affiliation:
Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany e-mails: clara.loeh@mathematik.uni-r.de, daniel.fauser@mathematik.uni-r.de
CLARA LÖH
Affiliation:
Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany e-mails: clara.loeh@mathematik.uni-r.de, daniel.fauser@mathematik.uni-r.de
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Functorial semi-norms on singular homology give refined ‘size’ information on singular homology classes. A fundamental example is the ℓ1-semi-norm. We show that there exist finite functorial semi-norms on singular homology that are exotic in the sense that they are not carried by the ℓ1-semi-norm.

MSC classification

Primary: 55N10: Singular theory
Secondary: 57N65: Algebraic topology of manifolds
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 2 , May 2019 , pp. 287 - 295
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

REFERENCES

1. Crowley, D. and Löh, C., Functorial semi-norms on singular homology and (in)flexible manifolds, Alg. Geom. Topol. 15 (3) (2015), 1453–1499.Google Scholar
2. Derbez, P., Local rigidity of aspherical three-manifolds, Annales de l'institut Fourier 62 (1) (2012), 393–416.Google Scholar
3. Derbez, P., Sun, H. and Wang, S., Finiteness of mapping degree sets for 3-manifolds, Acta Math. Sinica (Engl. Ser.) 27 (2011), 807–812.Google Scholar
4. Gromov, M., Volume and bounded cohomology, Publ. Math. IHES 56 (1982), 5–99.Google Scholar
5. Ivanov, N. V., Foundations of the theory of bounded cohomology, J. Sov. Math. 37 (1987), 1090–1115.Google Scholar
6. Kotschick, D. and Löh, C., Fundamental classes not representable by products, J. London Math. Soc. 79 (3) (2009), 545–561.Google Scholar
7. Kotschick, D., Löh, C. and Neofytidis, C., On stability of non-domination under taking products, Proc. Amer. Math. Soc. 144 (6) (2016), 2705–2710.Google Scholar
8. Löh, C., Isomorphisms in ℓ1-homology, Münster J. Math. 1 (2008), 237–266.Google Scholar
9. Löh, C., Simplicial volume, Bull. Man. Atl. (2011), 7–18.Google Scholar
10. Löh, C., Finite functorial semi-norms and representability, Int. Math. Res. Notices 2016 (12) (2016), 3616–3638.Google Scholar
11. Löh, C., Odd manifolds of small integral simplicial volume, to appear in Ark. Mat., arXiv: 1509.00204 [math.GT], 2015.Google Scholar
12. Neofytidis, C., Degrees of self-maps of products, Int. Math. Res. Notices 2017 (22) (2017), 6977–6989.Google Scholar
13. Thom, R., Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17–86.Google Scholar