Geodesic
Normed combinatorial homology and noncommutative tori
Theory and applications of categories, The Carboni Festschrift, Tome 13 (2004), pp. 114-128

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

Cubical sets have a directed homology, studied in a previous paper and consisting of preordered abelian groups, with a positive cone generated by the structural cubes. By this additional information, cubical sets can provide a sort of `noncommutative topology', agreeing with some results of noncommutative geometry but lacking the metric aspects of C* -algebras. Here, we make such similarity stricter by introducing normed cubical sets and their normed directed homology, formed of normed preordered abelian groups. The normed cubical sets NC_\theta associated with `irrational' rotations have thus the same classification up to isomorphism as the well-known irrational rotation C* -algebras A_\theta.

Classification : 55U10, 81R60, 55Nxx
Keywords: Cubical sets, noncommutative C*-algebras, combinatorial homology, normed abelian groups 
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     author = {Marco Grandis},
     title = {Normed combinatorial homology 
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     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2004_13_a6/}
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Marco Grandis. Normed combinatorial homology 
and noncommutative tori. Theory and applications of categories, The Carboni Festschrift, Tome 13 (2004), pp. 114-128. http://geodesic.mathdoc.fr/item/TAC_2004_13_a6/