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Abstract: We introduce a new simplicial nerve of higher dimensional automata whose homology groups yield a new definition of the globular homology. With this new definition, the drawbacks noticed with the construction of [Gau99] disappear. Moreover the important morphisms which associate to every globe its corresponding branching area and merging area of execution paths become morphisms of simplicial sets. (Update)
Context of citations to this paper: More
...composition properties of dipaths and of dihomotopies in an HDA. The interested reader can find the exploitation of these ideas in [19] [18] and [21] We will give the formal definition of an category in three steps (see for instance [7] 62] and [61] for more details) A...
.... where cubical sets with connections and compositions and their relationship with strict # categories are crucial; see Gaucher [58, 60]. This is related to a fundamental test property for definitions of n categories. It is known for some definitions (e.g. 78, 125,...
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Homotopy Branching Space and Weak Dihomotopy - Gaucher (Correct)
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BibTeX entry: (Update)
Gaucher, P., About the globular homology of higher dimensional automata (2000), arxiv:math.CT/0002216. http://citeseer.ist.psu.edu/gaucher00about.html More
@misc{ gaucher00about,
author = "P. Gaucher",
title = "About the globular homology of higher dimensional automata",
text = "Gaucher, P., About the globular homology of higher dimensional automata
(2000), arxiv:math.CT/0002216.",
year = "2000",
url = "citeseer.ist.psu.edu/gaucher00about.html" }
Citations (may not include all citations):96 Simplicial Objects in Algebraic Topology (context) - May - 1967
33 The algebra of oriented simplexes (context) - Street - 1987
21 Homotopy invariants of higher dimensional categories and con.. - Gaucher - 1999
6 The equivalence of 1-groupoids and crossed complexes (context) - Brown, Higgins - 1981
6 Ecole Normale Superieure (context) - Goubault, of et al. - 1995
4 eorie des ensembles (context) - Bourbaki - 1982
4 Tensor products of innity-categories (context) - Steiner - 1991
4 Simplicial methods and the interpretation of \triple (context) - Duskin - 1975
2 Classifying holes of arbitrary dimensions in partially order.. - Sokolowski - 1999
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.ipipan.gda.pl/~stefan/AlgTop/reports.html): More
From Concurrency to Algebraic Topology - Gaucher (2000) (Correct)
The Topological Structure of Asynchronous Computability - Herlihy, Shavit (1996) (Correct)
Detecting Deadlocks in Concurrent Systems - Fajstrup, Raußen (1996) (Correct)
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