scholarly journals Homotopy theory in toric topology

2016 ◽  
Vol 71 (2) ◽  
pp. 185-251 ◽  
Author(s):  
J Grbić ◽  
S Theriault
Keyword(s):  
Homotopy Theory ◽  
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.

On equivariant disconnected rational homotopy theory

2010 ◽  
Vol 17 (2) ◽  
pp. 229-240
Author(s):  
Marek Golasiński
Keyword(s):  
Homotopy Theory ◽  
Weak Equivalence ◽  
Rational Homotopy Theory ◽  
Rational Homotopy ◽  
Hamiltonian Group ◽  
Simplicial Set ◽  
De Rham

Abstract An equivariant disconnected Sullivan–de Rham equivalence is developed using Kan's result on diagram categories. Given a finite Hamiltonian group G, let X be a G-simplicial set. It is shown that the associated system of algebras indexed by the category 𝒪(G) of a canonical orbit can be “approximated” (up to a weak equivalence) by such a system ℳ X with the properties required by nonequivariant minimal algebras.

scholarly journals A First Approximation to Homotopy Theory

1953 ◽  
Vol 39 (7) ◽  
pp. 655-660 ◽  
Author(s):  
E. H. Spanier ◽  
J. H. C. Whitehead
Keyword(s):  
Homotopy Theory ◽  
First Approximation

scholarly journals Homotopy theory and generalized dimension subgroups

2017 ◽  
Vol 484 ◽  
pp. 224-246 ◽  
Author(s):  
Sergei O. Ivanov ◽  
Roman Mikhailov ◽  
Jie Wu
Keyword(s):  
Homotopy Theory ◽  
Generalized Dimension
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