Victor Chepoi's Books

Weakly Modular Graphs and Nonpositive Curvature

By: Jérémie Chalopin,Victor Chepoi,Hiroshi Hirai,Damian Osajda

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Weakly Modular Graphs and Nonpositive Curvature

By: Jérémie Chalopin,Victor Chepoi,Hiroshi Hirai,Damian Osajda

This article investigates structural, geometrical, and topological characteri-zations and properties of weakly modular graphs and of cell complexes derived from them. The unifying themes of our investigation are various “nonpositive cur-vature” and “local-to-global” properties and characterizations of weakly modular graphs and their subclasses. Weakly modular graphs have been introduced as a far-reaching common generalization of median graphs (and more generally, of mod-ular and orientable modular graphs), Helly graphs, bridged graphs, and dual polar graphs occurring under diﬀerent disguises (1–skeletons, collinearity graphs, covering graphs, domains, etc.) in several seemingly-unrelated ﬁelds of mathematics: * Metric graph theory * Geometric group theory * Incidence geometries and buildings * Theoretical computer science and combinatorial optimization We give a local-to-global characterization of weakly modular graphs and their sub-classes in terms of simple connectedness of associated triangle-square complexes and speciﬁc local combinatorial conditions. In particular, we revisit characterizations of dual polar graphs by Cameron and by Brouwer-Cohen. We also show that (disk-)Helly graphs are precisely the clique-Helly graphs with simply connected clique complexes. With l1–embeddable weakly modular and sweakly modular graphs we associate high-dimensional cell complexes, having several strong topological and geometrical properties (contractibility and the CAT(0) property). Their cells have a speciﬁc structure: they are basis polyhedra of even 􀀁–matroids in the ﬁrst case and orthoscheme complexes of gated dual polar subgraphs in the second case. We resolve some open problems concerning subclasses of weakly modular graphs: we prove a Brady-McCammond conjecture about CAT(0) metric on the orthoscheme.

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American Mathematical Soc.

Published Date

ISBN 10

1470443627

ISBN 13

9781470443627

The Winged Lion and the Eight-Pointed Cross

Venice, Hospitaller Malta, and the Mediterranean in Early Modern Times

By: Victor Mallia-Milanes

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The Winged Lion and the Eight-Pointed Cross

Venice, Hospitaller Malta, and the Mediterranean in Early Modern Times

By: Victor Mallia-Milanes

The papers reprinted in this volume focus on the extraordinary and multifaceted relationship between two Christian States: the Republic of Venice and the Island Order State on Hospitaller Malta between 1530 and the late 1790s. It was marked by three distinct phenomena – military cooperation along with other Western allies against the Ottoman Empire; direct mutual confrontation, at times even leading to war; and commercial cooperation. A fourth phenomenon, this time involving the wider Mediterranean context within which the two interacted, concerns the idea of decline. Some of the papers that follow question the validity of the traditional view that the Mediterranean and Venice were in decline by the sixteenth century and that the Hospitaller Order, claimed to be in decline by the eighteenth, had given up Malta to the French as a result. This book will appeal to all those interested in Crusading Orders and the history of the Crusades, as well as the history of Venice, Malta, and the Mediterranean in the early modern period.

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256

Publisher

Taylor & Francis

Published Date

ISBN 10

1000936287

ISBN 13

9781000936285

Weakly Modular Graphs and Nonpositive Curvature

By: Jérémie Chalopin,Victor Chepoi,Hiroshi Hirai,Damian Osajda

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Weakly Modular Graphs and Nonpositive Curvature

By: Jérémie Chalopin,Victor Chepoi,Hiroshi Hirai,Damian Osajda

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N/A

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Solve jigsaw puzzle

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Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470443627

ISBN 13

9781470443627

Book's by Victor Chepoi

Weakly Modular Graphs and Nonpositive Curvature

Weakly Modular Graphs and Nonpositive Curvature

The Winged Lion and the Eight-Pointed Cross

The Winged Lion and the Eight-Pointed Cross

Weakly Modular Graphs and Nonpositive Curvature

Weakly Modular Graphs and Nonpositive Curvature

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