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Toric objects associated with the dodecahedron

Toric objects associated with the dodecahedron
Toric objects associated with the dodecahedron

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 Poincaré series of the corresponding Pontryagin algebra.

Cohomology, Dodecahedron, Icosahedron, Moment-angle complex, Quasitoric manifolds, Small covers, Toric action
0354-5180
2329-2356
Baralić, Djordje
92f67760-1079-4f8f-b7fa-c504fa3e3fc3
Grbić, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175
Limonchenko, Ivan
4a608bf8-091e-4467-96de-a382486fa345
Vučić, Aleksandar
8c274ce2-5721-4637-ac29-7948665317bf
Baralić, Djordje
92f67760-1079-4f8f-b7fa-c504fa3e3fc3
Grbić, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175
Limonchenko, Ivan
4a608bf8-091e-4467-96de-a382486fa345
Vučić, Aleksandar
8c274ce2-5721-4637-ac29-7948665317bf

Baralić, Djordje, Grbić, Jelena, Limonchenko, Ivan and Vučić, Aleksandar (2020) Toric objects associated with the dodecahedron. Filomat, 34 (7), 2329-2356. (doi:10.2298/FIL2007329B).

Record type: Article

Abstract

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 Poincaré series of the corresponding Pontryagin algebra.

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Accepted/In Press date: 24 January 2020
e-pub ahead of print date: 17 December 2020
Keywords: Cohomology, Dodecahedron, Icosahedron, Moment-angle complex, Quasitoric manifolds, Small covers, Toric action

Identifiers

Local EPrints ID: 447812
URI: http://eprints.soton.ac.uk/id/eprint/447812
ISSN: 0354-5180
PURE UUID: 68dd8f83-7527-400d-9515-578ab780657f
ORCID for Jelena Grbić: ORCID iD orcid.org/0000-0002-7164-540X

Catalogue record

Date deposited: 23 Mar 2021 17:36
Last modified: 20 Jul 2022 01:47

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Contributors

Author: Djordje Baralić
Author: Jelena Grbić ORCID iD
Author: Ivan Limonchenko
Author: Aleksandar Vučić

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