6 papers
Total cut complexes and their duals
Andrés Carnero Bravo, Andrés Carnero Bravo
We study the total -cut complexes and their Alexander duals. We give some results about the connectivity in general and in terms of the grith of the graph. For , the hom…
Independence complexes of generalized Mycielskian graphs
Andrés Carnero Bravo
We show that the homotopy type of the independence complex of the generalized Mycielskian of a graph is determined by the homotopy type of the independence complex of and t…
Left and right Bousfield localization on lattices
Andrés Carnero Bravo, Shuchita Goyal, SofÃa MartÃnez Alberga +3
The key information of a model category structure on a poset is encoded in a transfer system, which is a combinatorial gadget, originally introduced to investigate homotopy coheren…
On independence complexes of graph products
Andrés Carnero Bravo
We study the independence complexes of graph products where at least one factor is a path. We also analyze the complexes of their induced subgraphs. We determine the homotopy type…
Polyhedral joins and graph complexes
Andrés Carnero Bravo
We give a decomposition of the suspension of a polyhedral join in terms of the polyhedral smash product of the suspension of the family of pairs, and study some cases in which the…
The Forest Filtration of a Graph
Andrés Carnero Bravo
Given a graph , we define a filtration of simplicial complexes associated to , where…