Open AccessToric objects associated with the dodecahedron
Author(s) -
Djordje Baralić,
Jelena Grbić,
Ivan Limonchenko,
Aleksandar Vučić
Publication year - 2020
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2007329b
Subject(s) - mathematics , dodecahedron , cohomology ring , homotopy , pure mathematics , manifold (fluid mechanics) , cohomology , cover (algebra) , ring (chemistry) , moment (physics) , algebra over a field , geometry , equivariant cohomology , mechanical engineering , chemistry , physics , organic chemistry , classical mechanics , engineering
In this paper we illustrate a tight interplay between homotopy theory and combinatorics within toric topology by explicitly calculating homotopy and combinatorial invariants of toric objects associated with the dodecahedron. In particular, we calculate the cohomology ring of the (complex and real) moment-angle manifolds over the dodecahedron, and of a certain quasitoric manifold and of a related small cover. We finish by studying Massey products in the cohomology ring of moment-angle manifolds over the dodecahedron and how the existence of nontrivial Massey products influences the behaviour of the Poincar? series of the corresponding Pontryagin algebra.