scholarly journals Massey products, toric topology and combinatorics of polytopes

2019 ◽  
Vol 83 (6) ◽  
pp. 1081-1136
Author(s):  
V. M. Buchstaber ◽  
I. Yu. Limonchenko
Keyword(s):  
Massey Products ◽  
Toric Topology

scholarly journals Toric objects associated with the dodecahedron

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2329-2356
Author(s):  
Djordje Baralic ◽  
Jelena Grbic ◽  
Ivan Limonchenko ◽  
Aleksandar Vucic
Keyword(s):  
Homotopy Theory ◽  
Cohomology Ring ◽  
Massey Products ◽  
Small Cover ◽  
Toric Topology ◽  
Quasitoric Manifold

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.

scholarly journals Higher order Massey products and applications

2021 ◽  
pp. 209-240
Author(s):  
Ivan Limonchenko ◽  
Dmitry Millionshchikov
Keyword(s):  
Lie Algebras ◽  
Homotopy Theory ◽  
Homology Theory ◽  
Higher Order ◽  
Local Rings ◽  
Main Theme ◽  
Massey Products ◽  
Research Areas ◽  
Cohomology Of Lie Algebras ◽  
Toric Topology

In this survey, we discuss two research areas related to Massey’s higher operations. The first direction is connected with the cohomology of Lie algebras and the theory of representations. The second main theme is at the intersection of toric topology, homotopy theory of polyhedral products, and the homology theory of local rings, Stanley–Reisner rings of simplicial complexes.

Massey products andH(p, q)-systems

1973 ◽  
Vol 132 (1) ◽  
pp. 1-10
Author(s):  
Donald M. Davis ◽  
Victor P. Snaith
Keyword(s):  
Massey Products

scholarly journals Compact symplectic manifolds with free circle actions, and Massey products.

1991 ◽  
Vol 38 (2) ◽  
pp. 271-283 ◽  
Author(s):  
Marisa Fernández ◽  
Alfred Gray ◽  
John W. Morgan
Keyword(s):  
Symplectic Manifolds ◽  
Circle Actions ◽  
Massey Products

Two Applications of Homology Decompositions

1975 ◽  
Vol 27 (2) ◽  
pp. 323-329 ◽  
Author(s):  
Graham Hilton Toomer
Keyword(s):  
Doctoral Dissertation ◽  
Massey Products ◽  
Cornell University ◽  
Future Paper

We show that a map of rational spaces (see Definition 1) induces a map of homology sections at each stage, and that the k'-invariants are mapped naturally. This is used to characterize rational spaces in which all (matric) Massey products vanish as wedges of rational spheres, and yields the precise Eckmann-Hilton dual of a result of M. Dyer [7]. Berstein's result on co-H spaces [3] is also deduced. These results form a part of the author's doctoral dissertation at Cornell University written under Professor I. Berstein, to whom I express my sincere thanks for his patient help and encouragement. Extensions and counterexamples will appear in a future paper.

Single-Valued Massey Products

2014 ◽  
Vol 42 (11) ◽  
pp. 4609-4618 ◽  
Author(s):  
Ido Efrat
Keyword(s):  
Massey Products
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