From: grandis@dima.unige.it (Marco Grandis)
To: categories@mta.ca
Subject: preprint: Normed combinatorial homology and noncommutative tori
Date: Wed, 23 Jul 2003 08:32:11 +0200 [thread overview]
Message-ID: <v02140b00bb43dbcf4f4f@[130.251.60.244]> (raw)
The following preprint is available in ps:
Normed combinatorial homology and noncommutative tori
Marco Grandis
Dip. Mat. Univ. Genova, Preprint 484 (Jul 2003), 14 p.
http://www.dima.unige.it/~grandis/Bsy2.ps
Abstract.
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 associated with
"irrational rotations" have thus the same classification up to isomorphism
as the well-known irrational rotation C*-algebras.
MSC: 55U10, 81R60, 55Nxx.
Keywords: Cubical sets, noncommutative C*-algebras, combinatorial homology,
normed abelian groups.
Marco Grandis
Dipartimento di Matematica
Universita` di Genova
via Dodecaneso 35
16146 GENOVA, Italy
e-mail: grandis@dima.unige.it
tel: +39.010.353 6805 fax: +39.010.353 6752
http://www.dima.unige.it/~grandis/
next reply other threads:[~2003-07-23 6:32 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2003-07-23 6:32 Marco Grandis [this message]
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2003-07-18 12:39 Marco Grandis
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