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Foundations of a Connectivity Theory for Simplicial Complexes

✍ Scribed by Hélène Barcelo; Xenia Kramer; Reinhard Laubenbacher; Christopher Weaver

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
422 KB
Volume
26
Category
Article
ISSN
0196-8858

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✦ Synopsis

This paper lays the foundations of a combinatorial homotopy theory, called A-theory, for simplicial complexes, which reflects their connectivity properties. A collection of bigraded groups is constructed, and methods for computation are given. A Seifert-Van Kampen type theorem and a long exact sequence of relative A-groups are derived. A related theory for graphs is constructed as well. This theory provides a general framework encompassing homotopy methods used to prove connectivity results about buildings, graphs, and matroids.

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