no. 12
Combinatorics/Topology
Connectivity of pseudomanifold graphs from an algebraic point of view
[Connexité des graphes de pseudo-variétés d'un point de vue algébrique]

Présenté par : the Editorial Board

Adiprasito, Karim A.1, 2 ; Goodarzi, Afshin3 ; Varbaro, Matteo4
1 Institut des hautes études scientifiques, Bures-sur-Yvette, France
2 Einstein Institute for Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel
3 Department of Mathematics, Kungliga Tekniska Högskolan, S-100 44 Stockholm, Sweden
4 Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35-16146, Genova, Italy
Comptes Rendus. Mathématique, Tome 353 (2015) no. 12, pp. 1061-1065.

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 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.

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Accepté le :
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DOI : 10.1016/j.crma.2015.09.018
Adiprasito, Karim A. 1, 2 ; Goodarzi, Afshin 3 ; Varbaro, Matteo 4

1 Institut des hautes études scientifiques, Bures-sur-Yvette, France
2 Einstein Institute for Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel
3 Department of Mathematics, Kungliga Tekniska Högskolan, S-100 44 Stockholm, Sweden
4 Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35-16146, Genova, Italy 
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Adiprasito, Karim A.; Goodarzi, Afshin; Varbaro, Matteo. Connectivity of pseudomanifold graphs from an algebraic point of view. Comptes Rendus. Mathématique, Tome 353 (2015) no. 12, pp. 1061-1065. doi : 10.1016/j.crma.2015.09.018. http://www.numdam.org/articles/10.1016/j.crma.2015.09.018/

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