## 8 Citations

Two-dimensional Golod complexes

- Mathematics
- 2020

We characterize two-dimensional Golod complexes combinatorially by vertex-breakability and topologically by the fat-wedge filtration of a polyhedral product. Applying the characterization, we…

Golod and tight 3-manifolds

- Mathematics
- 2021

The notions Golodness and tightness for simplicial complexes come from algebra and geometry, respectively. We prove these two notions are equivalent for 3-manifold triangulations, through a…

Higher order Massey products and applications

- MathematicsTopology, Geometry, and Dynamics
- 2021

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…

Polyhedral products and features of their homotopy theory

- MathematicsHandbook of Homotopy Theory
- 2020

A polyhedral product is a natural subspace of a Cartesian product that is specified by a simplicial complex. The modern formalism arose as a generalization of the spaces known as moment-angle…

LS-category of moment-angle manifolds and higher order Massey products

- MathematicsForum Mathematicum
- 2021

Abstract Using the combinatorics of the underlying simplicial complex K, we give various upper and lower bounds for the Lusternik–Schnirelmann (LS) category of moment-angle complexes…

Massey products, toric topology and combinatorics of polytopes

- MathematicsIzvestiya: Mathematics
- 2019

In this paper we introduce a direct family of simple polytopes P 0 ⊂ P 1 ⊂ . . . such that for any 2 ≤ k ≤ n there are non-trivial strictly defined Massey products of order k in the cohomology rings…

Massey products, toric topology and combinatorics of polytopes

- Mathematics
- 2019

In this paper we introduce a direct family of simple polytopes $P^{0}\subset P^{1}\subset\ldots$ such that for any $k$, $2\leq k\leq n$ there are non-trivial strictly defined Massey products of order…

One-relator groups and algebras related to polyhedral products

- MathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
- 2022

We link distinct concepts of geometric group theory and homotopy theory through underlying combinatorics. For a flag simplicial complex $K$, we specify a necessary and sufficient combinatorial…

## References

SHOWING 1-10 OF 27 REFERENCES

Homotopy types of moment-angle complexes for flag complexes

- Mathematics
- 2012

We study the homotopy types of moment-angle complexes, or equivalently, of complements of coordinate subspace arrangements. The overall aim is to identify the simplicial complexes K for which the…

Note: Combinatorial Alexander Duality—A Short and Elementary Proof

- MathematicsDiscret. Comput. Geom.
- 2009

A self-contained proof from first principles accessible to a nonexpert is given that the combinatorial Alexander duality of X is isomorphic to the (|V|−i−3)th reduced cohomology group of X* (over a given commutative ring R).

The integral cohomology of toric manifolds

- Mathematics
- 2006

We prove that the integral cohomology of a smooth, not necessarily compact, toric variety XΣ is determined by the Stanley-Reisner ring of Σ. This follows from a formality result for singular cochains…

A Minimal Triangulation of the Hopf Map and its Application

- Mathematics
- 2000

We give a minimal triangulation η: S123→S42 of the Hopf map h: S3→S2 and use it to obtain a new construction of the 9-vertex complex projective plane.

Decompositions of suspensions of spaces involving polyhedral products

- Mathematics
- 2015

Two homotopy decompositions of supensions of spaces involving polyhedral products are given. The first decomposition is motivated by the decomposition of suspensions of polyhedral products by Bahri,…

The polyhedral product functor: a method of computation for moment-angle complexes, arrangements and related spaces

- Mathematics
- 2007

Fat-wedge filtration and decomposition of polyhedral products

- MathematicsKyoto Journal of Mathematics
- 2019

The polyhedral product constructed from a collection of pairs of cones and their bases and a simplicial complex $K$ is studied by investigating its filtration called the fat wedge filtration. We give…

Algebraic Topology

- Mathematics

The focus of this paper is a proof of the Nielsen-Schreier Theorem, stating that every subgroup of a free group is free, using tools from algebraic topology.