Geodesic
Spec(Z) and the Gromov Norm
Theory and applications of categories, Tome 35 (2020), pp. 155-178

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We define the homology of a simplicial set with coefficients in a Segal's Gamma-set (s-module). We show the relevance of this new homology with values in s-modules by proving that taking as coefficients the s-modules at the archimedean place over the structure sheaf on Spec(Z), one obtains on the singular homology with real coefficients of a topological space X, a norm equivalent to the Gromov norm. Moreover, we prove that the two norms agree when X is an oriented compact Riemann surface.

Publié le :
Classification : 16Y60, 20N20, 18G55, 18G30, 18G35, 18G55, 18G60, 14G40
Keywords: Gamma spaces, Gamma rings, Site, Gromov norm, Arakelov geometry, Homology theory 
@article{TAC_2020_35_a5,
     author = {Alain Connes and Caterina Consani},
     title = {Spec(Z) and the {Gromov} {Norm}},
     journal = {Theory and applications of categories},
     pages = {155--178},
     publisher = {mathdoc},
     volume = {35},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a5/}
}
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Alain Connes; Caterina Consani. Spec(Z) and the Gromov Norm. Theory and applications of categories, Tome 35 (2020), pp. 155-178. http://geodesic.mathdoc.fr/item/TAC_2020_35_a5/