Normed combinatorial homology and noncommutative tori (*)
نویسنده
چکیده
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 NCθ associated with 'irrational' rotations have thus the same classification up to isomorphism as the well-known irrational rotation C*-algebras Aθ. MSC: 55U10, 81R60, 55Nxx.
منابع مشابه
NORMED COMBINATORIAL HOMOLOGY AND NONCOMMUTATIVE TORI Dedicated to Aurelio Carboni on the occasion of his sixtieth birthday
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 stri...
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