Simplicial volume via normalised cycles
Authors:
Clara Löh and Marco Moraschini
Journal:
Proc. Amer. Math. Soc. 148 (2020), 5437-5440
MSC (2020):
Primary 55N10, 57N65, 18N50, 18G35, 18G90
DOI:
https://doi.org/10.1090/proc/15201
Published electronically:
September 11, 2020
MathSciNet review:
4163854
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Abstract | References | Similar Articles | Additional Information
Abstract: We show that the Connes-Consani semi-norm on singular homology with real coefficients, defined via s-modules, coincides with the ordinary $\ell ^1$-semi-norm on singular homology in all dimensions.
- A. Connes and C. Consani, $\overline {\mathrm {Spec}\; \mathbb {Z}}$ and the Gromov norm, Theory Appl. Categories 35 (2020), no. 6, 155–178.
- Koji Fujiwara and Jason Fox Manning, Simplicial volume and fillings of hyperbolic manifolds, Algebr. Geom. Topol. 11 (2011), no. 4, 2237–2264. MR 2826938, DOI https://doi.org/10.2140/agt.2011.11.2237
- Michael Gromov, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. 56 (1982), 5–99 (1983). MR 686042
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Additional Information
Clara Löh
Affiliation:
Fakultät für Mathematik, Universität Regensburg, Regensburg, Germany
MR Author ID:
780073
ORCID:
0000-0003-0228-2585
Email:
clara.loeh@ur.de
Marco Moraschini
Affiliation:
Fakultät für Mathematik, Universität Regensburg, Regensburg, Germany
MR Author ID:
1143899
ORCID:
0000-0003-2692-6584
Email:
marco.moraschini@ur.de
Keywords:
Simplicial volume,
semi-norms on homology,
s-modules
Received by editor(s):
March 11, 2020
Published electronically:
September 11, 2020
Additional Notes:
This work was supported by the CRC 1085 Higher Invariants (Universität Regensburg, funded by the DFG)
Communicated by:
Julia Bergner
Article copyright:
© Copyright 2020
American Mathematical Society
