2012/06/15 by Elías Gabriel Minian, Elias Gabriel Minian, Jorge Tomás Rodríguez +3
Mathematics · #06A06 #55M05 #55P15 #55U05 #57Q05 #57Q10 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #math.CO #msc:06A06 #msc:55M05 #msc:55P15 #msc:55U05 #msc:57Q05 #msc:57Q10
paper · pdf · doi:10.48550/arxiv.1206.3368
6 pages
arxiv created 2012/06/15 · openalex publication_date 2012/06/15 · arxiv updated 2012/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the homotopy type of the Alexander dual of a simplicial complex. In general the homotopy type of K does not determine the homotopy type of its dual K*. Moreover, one can construct for each finitely presented group G, a simply connected simplicial complex K with fundamental group isomorphic to G. We study sufficient conditions on K for K* to have the homotopy type of a sphere. We also extend the simplicial Alexander duality to the context of reduced lattices.