| Title: | Bucolic complexes |
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| Authors: | ID Brešar, Boštjan (Author)
ID Chalopin, Jérémie (Author)
ID Chepoi, Victor (Author)
ID Dravec, Tanja (Author)
ID Osajda, Damian (Author) |
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| Files: |  http://www.imfm.si/preprinti/PDF/01171.pdf
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| Language: | English |
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| Work type: | Not categorized (r6) |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
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| Abstract: | In this article, we introduce and investigate bucolic complexes, a common generalization of systolic complexes and of CAT(0) cubical complexes. This class of complexes is closed under Cartesian products and amalgamations over some convex subcomplexes. We study various approaches to bucolic complexes: from graph-theoretic and topological viewpoints, as well as from the point of view of geometric group theory. Bucolic complexes can be defined as locally-finite simply connected prism complexes satisfying some local combinatorial conditions. We show that bucolic complexes are contractible, and satisfy some nonpositive-curvature-like properties. In particular, we prove a version of the Cartan-Hadamard theorem, the fixed point theorem for finite group actions, and establish some results on groups acting geometrically on such complexes. We also characterize the 1-skeletons (which we call bucolic graphs) and the 2-skeletons of bucolic complexes. In particular, we prove that bucolic graphs are precisely retracts of Cartesian products of locally finite weakly bridged graphs (i.e., of 1-skeletons of weakly systolic complexes). We show that bucolic graphs are exactly the weakly modular graphs satisfying some local conditions formulated in terms of forbidden induced subgraphs and that finite bucolic graphs can be obtained by gated amalgamations of products of weakly bridged graphs. |
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| Keywords: | CAT(0) kubni in sistolični kompleksi, medianski in mostovni grafi, zastražena amalgamacija, kartezični produkt, prizmični kompleksi, retrakti, fiksne točke, asferičnost, CAT(0) cubical and systolic complexes, median and bridged graphs, gated amalgamation, Cartesian product, prism complexes, retracts, fixed points, asphericity |
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| Year of publishing: | 2012 |
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| Number of pages: | str. 1-24 |
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| Numbering: | Vol. 50, št. 1171 |
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| PID: | 20.500.12556/DKUM-51983  |
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| UDC: | 519.17:512.5 |
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| ISSN on article: | 2232-2094 |
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| COBISS.SI-ID: | 16207961 |
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| NUK URN: | URN:SI:UM:DK:WX5QC9R4 |
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| Publication date in DKUM: | 10.07.2015 |
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| Views: | 768 |
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| Downloads: | 19 |
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| Metadata: |     |
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| Categories: | Misc.
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