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Comptes Rendus Mathématique
Volume 353, n° 12
pages 1061-1065 (décembre 2015)
Doi : 10.1016/j.crma.2015.09.018
Received : 4 November 2014 ;  accepted : 22 September 2015
Connectivity of pseudomanifold graphs from an algebraic point of view
Connexité des graphes de pseudo-variétés d'un point de vue algébrique
 

Karim A. Adiprasito a, b, 1 , Afshin Goodarzi c , Matteo Varbaro d, 2
a Institut des hautes études scientifiques, Bures-sur-Yvette, France 
b Einstein Institute for Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel 
c Department of Mathematics, Kungliga Tekniska Högskolan, S-100 44 Stockholm, Sweden 
d Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35-16146, Genova, Italy 

Abstract

The connectivity of graphs of simplicial and polytopal complexes is a classical subject going back at least to Steinitz, and the topic has since been studied by many authors, including Balinski, Barnette, Athanasiadis, and Björner. In this note, we provide a unifying approach that allows us to obtain more general results. Moreover, we provide a relation to commutative algebra by relating connectivity problems to graded Betti numbers of the associated Stanley–Reisner rings.

The full text of this article is available in PDF format.
Résumé

La connexité des graphes des complexes simpliciaux et polytopaux est un sujet classique remontant au moins à Steinitz. Il a été étudié depuis par de nombreux auteurs, dont Balinski, Barnette, Athanasiadis et Björner. Dans cette note, nous présentons une approche unifiée nous permettant d'obtenir des résultats plus généraux. De plus, nous faisons un lien avec l'algèbre commutative en rapprochant les problèmes de connexité des nombres de Betti gradués des anneaux de Stanley–Reisner associés.

The full text of this article is available in PDF format.
1  K. Adiprasito was supported by an EPDI/IPDE postdoctoral fellowship and a Minerva fellowship of the Max Planck Society.
2  M. Varbaro was supported by PRIN 2010S47ARA_003 “Geometria delle Varietà Algebriche”.


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